NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes
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Page 1
NCERT
SOLUTIONS
CLASS - 6TH
aglase .co
SOLUTIONS
CLASS - 6TH
aglase .co
Page 2
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
Class : 6th
Subject : Maths
Chapter : 5
Chapter Name : UNDERSTANDING ELEMENTARY SHAPES
Exercise 5.1
Q1 What is the disadvantage in comparing line segments by mere observation?
Answer. By mere observation, we cannot be absolutely sure about the judgement. When we
compare two line segments of almost same lengths, we cannot be sure about the line segment
of greater length. Therefore, it's not an appropriate method to compare line segments having a
slight difference between their lengths. This is the disadvantage in comparing line segments bv
mere observation.
Page : 88 , Block Name : Exercise 5.1
Q2 Why is it better to use a divider than a ruler, while measuring the length of a line segment?
Answer. It is better to use a divider than a ruler because while using a ruler, positioning error
may occur due to the incorrect positioning of the eye.
Page : 88 , Block Name : Exercise 5.1
¯¯¯¯¯¯¯¯
Q3 Draw any line segment, say AB. Take any point C lying in between A and B. Measure the
lengths of AB, BC and AC. Is AB = AC + CB?
[Note : If A,B,C are any three points on a line such that AC + CB = AB, then we can be sure that
C lies between A and B.]
Answer. It Is given that point C Is lying somewhere in between A and B. Therefore, all these
¯¯¯¯¯¯¯¯
points are lying on the same line segment AB. Hence, for every situation in which point C is
lying in between A and B, It may be said that AB = AC + CB.
For example,
¯¯¯¯¯¯¯¯
AB is a line segment of 6 cm and C is a point between A and B, such that it is 2 cm away from
¯¯¯¯¯¯¯¯
point B. We can �nd that the measure of line segment AC comes to 4 cm.
Hence, relation AB = AC + CB is veri�ed.
Page : 88 , Block Name : Exercise 5.1
Q4 If A,B,C are three points on a line such that AB = 5 cm, BC = 3 cm and AC = 8 cm, which one
of them lies between the other two?
Page 1 of 23 Aglasem Schools
Class : 6th
Subject : Maths
Chapter : 5
Chapter Name : UNDERSTANDING ELEMENTARY SHAPES
Exercise 5.1
Q1 What is the disadvantage in comparing line segments by mere observation?
Answer. By mere observation, we cannot be absolutely sure about the judgement. When we
compare two line segments of almost same lengths, we cannot be sure about the line segment
of greater length. Therefore, it's not an appropriate method to compare line segments having a
slight difference between their lengths. This is the disadvantage in comparing line segments bv
mere observation.
Page : 88 , Block Name : Exercise 5.1
Q2 Why is it better to use a divider than a ruler, while measuring the length of a line segment?
Answer. It is better to use a divider than a ruler because while using a ruler, positioning error
may occur due to the incorrect positioning of the eye.
Page : 88 , Block Name : Exercise 5.1
¯¯¯¯¯¯¯¯
Q3 Draw any line segment, say AB. Take any point C lying in between A and B. Measure the
lengths of AB, BC and AC. Is AB = AC + CB?
[Note : If A,B,C are any three points on a line such that AC + CB = AB, then we can be sure that
C lies between A and B.]
Answer. It Is given that point C Is lying somewhere in between A and B. Therefore, all these
¯¯¯¯¯¯¯¯
points are lying on the same line segment AB. Hence, for every situation in which point C is
lying in between A and B, It may be said that AB = AC + CB.
For example,
¯¯¯¯¯¯¯¯
AB is a line segment of 6 cm and C is a point between A and B, such that it is 2 cm away from
¯¯¯¯¯¯¯¯
point B. We can �nd that the measure of line segment AC comes to 4 cm.
Hence, relation AB = AC + CB is veri�ed.
Page : 88 , Block Name : Exercise 5.1
Q4 If A,B,C are three points on a line such that AB = 5 cm, BC = 3 cm and AC = 8 cm, which one
of them lies between the other two?
Page 1 of 23 Aglasem Schools
Page 3
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
Answer. Given that,
AB = 5 cm
BC = 3 cm
AC = 8 cm
It can be observed that AC = AB + BC
Clearly, point B is lying between A and C.
Page : 89 , Block Name : Exercise 5.1
¯¯¯¯¯¯¯¯
Q5 Verify, whether D is the mid point of AG .
Answer. From the given �gure, it can be observed that
¯¯¯¯¯¯¯¯
AD = 4 − 1 = 3 units
¯¯¯¯¯¯¯¯¯
DG = 7 − 4 = 3 units
¯¯¯¯¯¯¯¯
AG = 7 − 1 = 6units units
Clearly, D is the mid-point of AG.
Page : 89 , Block Name : Exercise 5.1
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q6 If B is the mid point of AC and C is the mid point of BD, where A,B,C,D lie on a straight
line, say why AB = CD?
Answer.
Since B is the mid-point of AC,
AB = BC (1)
Since C is the mid-point of BD,
BC = CD (2)
From equation (1) and (2), we may �nd that
AB = CD
Page : 89 , Block Name : Exercise 5.1
Q7 Draw �ve triangles and measure their sides. Check in each case, if the sum of the lengths of
any two sides is always less than the third side.
Answer. Yes, sum of two sides of a triangle is always greater than the third side.
Page 2 of 23 Aglasem Schools
Answer. Given that,
AB = 5 cm
BC = 3 cm
AC = 8 cm
It can be observed that AC = AB + BC
Clearly, point B is lying between A and C.
Page : 89 , Block Name : Exercise 5.1
¯¯¯¯¯¯¯¯
Q5 Verify, whether D is the mid point of AG .
Answer. From the given �gure, it can be observed that
¯¯¯¯¯¯¯¯
AD = 4 − 1 = 3 units
¯¯¯¯¯¯¯¯¯
DG = 7 − 4 = 3 units
¯¯¯¯¯¯¯¯
AG = 7 − 1 = 6units units
Clearly, D is the mid-point of AG.
Page : 89 , Block Name : Exercise 5.1
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q6 If B is the mid point of AC and C is the mid point of BD, where A,B,C,D lie on a straight
line, say why AB = CD?
Answer.
Since B is the mid-point of AC,
AB = BC (1)
Since C is the mid-point of BD,
BC = CD (2)
From equation (1) and (2), we may �nd that
AB = CD
Page : 89 , Block Name : Exercise 5.1
Q7 Draw �ve triangles and measure their sides. Check in each case, if the sum of the lengths of
any two sides is always less than the third side.
Answer. Yes, sum of two sides of a triangle is always greater than the third side.
Page 2 of 23 Aglasem Schools
Page 4
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
Page : 89 , Block Name : Exercise 5.1
Exercise 5.2
Q1 What fraction of a clockwise revolution does the hour hand of a clock turn through, when it
goes from
(a) 3 to 9
(b) 4 to 7
(c) 7 to 10
(d) 12 to 9
(e) 1 to 10
(f) 6 to 3
Answer. We may observe that in 1 complete clockwise revolution, the hour hand will
Page 3 of 23 Aglasem Schools
Page : 89 , Block Name : Exercise 5.1
Exercise 5.2
Q1 What fraction of a clockwise revolution does the hour hand of a clock turn through, when it
goes from
(a) 3 to 9
(b) 4 to 7
(c) 7 to 10
(d) 12 to 9
(e) 1 to 10
(f) 6 to 3
Answer. We may observe that in 1 complete clockwise revolution, the hour hand will
Page 3 of 23 Aglasem Schools
Page 5
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
rotate by 360∘ .
(a) When the hour hand goes from 3 to 9 clockwise, It will rotate bv 2 right angles or
180∘ .
∘
Fraction = 180
360∘
= 12
(b) When the hour hand goes from 4 to 7 clockwise, it will rotate by 1 right angle or 90∘ .
∘
90 1
Fraction = 360 ∘ =
4
(c) When the hour hand goes from 7 to 10 clockwise, It will rotate by 1 right angle or 90∘
∘
90 1
Fraction = 360 ∘ =
4
(d) When the hour hand goes from 12 to 9 clockwise, it will rotate by 3 right angles or 270∘
∘
3
Fraction = 270
360∘
= 4
(e) When the hour hand goes from 1 to 10 clockwise, it will rotate by 3 right angles or 270∘
∘
3
Fraction = 270
360∘
= 4
(f) When the hour hand goes from 6 to 3 clockwise, it will rotate bv 3 right angles or 270∘
∘
3
Fraction = 270
360∘
= 4
Page : 91 , Block Name : Exercise 5.2
Q2 Where will the hand of a clock stop if it
(a) starts at 12 and makes 1/2 of a revolution, clockwise?
(b) starts at 2 and makes 1/2 of a revolution, clockwise?
(c) starts at 5 and makes 1/4 of a revolution, clockwise?
Page 4 of 23 Aglasem Schools
rotate by 360∘ .
(a) When the hour hand goes from 3 to 9 clockwise, It will rotate bv 2 right angles or
180∘ .
∘
Fraction = 180
360∘
= 12
(b) When the hour hand goes from 4 to 7 clockwise, it will rotate by 1 right angle or 90∘ .
∘
90 1
Fraction = 360 ∘ =
4
(c) When the hour hand goes from 7 to 10 clockwise, It will rotate by 1 right angle or 90∘
∘
90 1
Fraction = 360 ∘ =
4
(d) When the hour hand goes from 12 to 9 clockwise, it will rotate by 3 right angles or 270∘
∘
3
Fraction = 270
360∘
= 4
(e) When the hour hand goes from 1 to 10 clockwise, it will rotate by 3 right angles or 270∘
∘
3
Fraction = 270
360∘
= 4
(f) When the hour hand goes from 6 to 3 clockwise, it will rotate bv 3 right angles or 270∘
∘
3
Fraction = 270
360∘
= 4
Page : 91 , Block Name : Exercise 5.2
Q2 Where will the hand of a clock stop if it
(a) starts at 12 and makes 1/2 of a revolution, clockwise?
(b) starts at 2 and makes 1/2 of a revolution, clockwise?
(c) starts at 5 and makes 1/4 of a revolution, clockwise?
Page 4 of 23 Aglasem Schools
Page 6
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
(d) starts at 5 and makes 3/4 of a revolution, clockwise?
Answer. In complete clockwise revolution, the hand of a clock will rotate by 360∘
(a) If the hand of the clock starts at 12 and makes 1/2 of a revolution clockwise, then it will
rotate by 180∘ and hence, it will stop at 6.
(b) If the hand of the clock starts at 2 and makes 1/2 of a revolution clockwise, then it will rotate
by 180∘ and hence, it will stop at 8.
(c) If the hand of the clock starts at S and makes 1/4 of a revolution clockwise, then it will rotate
by 90∘ and hence, it will stop at 8.
(d) If the hand Of the Clock StartS at 5 and makes 3/4 Of a revolution Clockwise, then it Will
rotate by 270∘ and hence, It will stop at 2.
Page : 91 , Block Name : Exercise 5.2
Q3 Which direction will you face if you start facing
(a) east and make 1/2 of a revolution clockwise?
(b) east and make 1 12 of a revolution clockwise?
(c) west and make 3/4 of a revolution anti-clockwise?
(d) south and make one full revolution?
(Should we specify clockwise or anti-clockwise for this last question? Why not?)
Answer. If revolve one complete round in either clockwise or anti-clockwise direction, then we
Page 5 of 23 Aglasem Schools
(d) starts at 5 and makes 3/4 of a revolution, clockwise?
Answer. In complete clockwise revolution, the hand of a clock will rotate by 360∘
(a) If the hand of the clock starts at 12 and makes 1/2 of a revolution clockwise, then it will
rotate by 180∘ and hence, it will stop at 6.
(b) If the hand of the clock starts at 2 and makes 1/2 of a revolution clockwise, then it will rotate
by 180∘ and hence, it will stop at 8.
(c) If the hand of the clock starts at S and makes 1/4 of a revolution clockwise, then it will rotate
by 90∘ and hence, it will stop at 8.
(d) If the hand Of the Clock StartS at 5 and makes 3/4 Of a revolution Clockwise, then it Will
rotate by 270∘ and hence, It will stop at 2.
Page : 91 , Block Name : Exercise 5.2
Q3 Which direction will you face if you start facing
(a) east and make 1/2 of a revolution clockwise?
(b) east and make 1 12 of a revolution clockwise?
(c) west and make 3/4 of a revolution anti-clockwise?
(d) south and make one full revolution?
(Should we specify clockwise or anti-clockwise for this last question? Why not?)
Answer. If revolve one complete round in either clockwise or anti-clockwise direction, then we
Page 5 of 23 Aglasem Schools
Page 7
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
will revolve by 360∘ and the two adjacent directions will be at 90∘ or 1/4 of a complete
revolution away from each other.
(a) If start facing East and make 1/2 of a revolution clockwise, then we will face the
West direction.
(b) If we start facing East and make 1 12 of a revolution clockwise, then we will face the West
direction.
(c) If start facing West and make 3/4 of a revolution anti-clockwise, then we will face
the North direction.
(d) If we start facing South and make a full revolution, then we will again
face the South direction.
In case of revolving by 1 complete round, the direction in which we are revolving does
not matter. In both cases, clockwise or anti-clockwise, we will be back at our initial
position.
Page : 91 , Block Name : Exercise 5.2
Q4 What part of a revolution have you turned through if you stand facing
Page 6 of 23 Aglasem Schools
will revolve by 360∘ and the two adjacent directions will be at 90∘ or 1/4 of a complete
revolution away from each other.
(a) If start facing East and make 1/2 of a revolution clockwise, then we will face the
West direction.
(b) If we start facing East and make 1 12 of a revolution clockwise, then we will face the West
direction.
(c) If start facing West and make 3/4 of a revolution anti-clockwise, then we will face
the North direction.
(d) If we start facing South and make a full revolution, then we will again
face the South direction.
In case of revolving by 1 complete round, the direction in which we are revolving does
not matter. In both cases, clockwise or anti-clockwise, we will be back at our initial
position.
Page : 91 , Block Name : Exercise 5.2
Q4 What part of a revolution have you turned through if you stand facing
Page 6 of 23 Aglasem Schools
Page 8
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
(a) east and turn clockwise to face north?
(b) south and turn clockwise to face east?
(c) west and turn clockwise to face east?
Answer. If we revolve one complete round in either clockwise or anti-clockwise direction, then
we
will revolve by 360∘ and the two adjacent directions will be at 90∘ or 1/4 of a complete
revolution away from each other.
(a) If Start facing turn Clockwise to face North, then have to make 3/4 of a
revolution.
(b) If we start facing South and turn clockwise to face east, then we have to make 3/4 of a
revolution.
(c) If We Start facing West and turn Clockwise to face East, then have to make 1/2 of a
revolution,
Page : 91 , Block Name : Exercise 5.2
Q5 Find the number of right angles turned through by the hour hand of a clock when it goes
from
(a) 3 to 6
(b) 2 to 8
(c) 5 to 11
(d) 10 to 1
(e) 12 to 9
(f) 12 to 6
Page 7 of 23 Aglasem Schools
(a) east and turn clockwise to face north?
(b) south and turn clockwise to face east?
(c) west and turn clockwise to face east?
Answer. If we revolve one complete round in either clockwise or anti-clockwise direction, then
we
will revolve by 360∘ and the two adjacent directions will be at 90∘ or 1/4 of a complete
revolution away from each other.
(a) If Start facing turn Clockwise to face North, then have to make 3/4 of a
revolution.
(b) If we start facing South and turn clockwise to face east, then we have to make 3/4 of a
revolution.
(c) If We Start facing West and turn Clockwise to face East, then have to make 1/2 of a
revolution,
Page : 91 , Block Name : Exercise 5.2
Q5 Find the number of right angles turned through by the hour hand of a clock when it goes
from
(a) 3 to 6
(b) 2 to 8
(c) 5 to 11
(d) 10 to 1
(e) 12 to 9
(f) 12 to 6
Page 7 of 23 Aglasem Schools
Page 9
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
Answer. The hour hand of a clock revolves by 360∘ or 4 right angles in Complete round.
(a) The hour hand of a clock revolves 90∘ or 1 right angle when It goes from 3 to 6.
(b) The hour hand of a clock revolves by 180∘ or 2 right angles when it goes from 2 to 8.
(c) The hour hand of a clock revolves by 180∘ or 2 right angles when it goes from 5 to 11.
(d) The hour hand of a clock revolves by 90∘ or 1 right angle when It goes from 10 to 1.
(e) The hour hand of a clock revolves bv 270∘ or 3 right angles when it goes fmm 12 to 9
(f) The hour hand cf a clock revolves by 180∘ or 2 right angles when It goes from 12 to 6
Page : 91 , Block Name : Exercise 5.2
Q6 How many right angles do you make if you start facing
(a) south and turn clockwise to west?
(b) north and turn anti-clockwise to east?
(c) west and turn to west?
(d) south and turn to north?
Answer. It revolve one complete round in either clockwise or anti-clockwise direction, then we
will revolve by 360∘ or 4 right angles and the two adjacent directions will be at 90∘ or 1 right
angle away from each other.
(a) If we start facing South and turn clockwise to West. then we make 1 right angle.
Page 8 of 23 Aglasem Schools
Answer. The hour hand of a clock revolves by 360∘ or 4 right angles in Complete round.
(a) The hour hand of a clock revolves 90∘ or 1 right angle when It goes from 3 to 6.
(b) The hour hand of a clock revolves by 180∘ or 2 right angles when it goes from 2 to 8.
(c) The hour hand of a clock revolves by 180∘ or 2 right angles when it goes from 5 to 11.
(d) The hour hand of a clock revolves by 90∘ or 1 right angle when It goes from 10 to 1.
(e) The hour hand of a clock revolves bv 270∘ or 3 right angles when it goes fmm 12 to 9
(f) The hour hand cf a clock revolves by 180∘ or 2 right angles when It goes from 12 to 6
Page : 91 , Block Name : Exercise 5.2
Q6 How many right angles do you make if you start facing
(a) south and turn clockwise to west?
(b) north and turn anti-clockwise to east?
(c) west and turn to west?
(d) south and turn to north?
Answer. It revolve one complete round in either clockwise or anti-clockwise direction, then we
will revolve by 360∘ or 4 right angles and the two adjacent directions will be at 90∘ or 1 right
angle away from each other.
(a) If we start facing South and turn clockwise to West. then we make 1 right angle.
Page 8 of 23 Aglasem Schools
Page 10
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
(b) If We Start facing North and anti-clockwise to East, then make 3 right angles.
(c) If we star facing West and turn to West, then make 1 complete round or 4 right
angles.
(d) If start facing South and turn to North, then make 2 right angles.
Page : 92 , Block Name : Exercise 5.2
Q7 Where will the hour hand of a clock stop if it starts
(a) from 6 and turns through 1 right angle?
(b) from 8 and turns through 2 right angles?
(c) from 10 and turns through 3 right angles?
(d) from 7 and turns through 2 straight angles?
Answer. In 1 complete revolution (clockwise or anti-clockwise), the hour hand of a clock will
rotate by 360∘ or 4 right angles.
(a) the hour hand of a clock starts from 6 and tums through 1 right angle, then it
stop at 9.
Page 9 of 23 Aglasem Schools
(b) If We Start facing North and anti-clockwise to East, then make 3 right angles.
(c) If we star facing West and turn to West, then make 1 complete round or 4 right
angles.
(d) If start facing South and turn to North, then make 2 right angles.
Page : 92 , Block Name : Exercise 5.2
Q7 Where will the hour hand of a clock stop if it starts
(a) from 6 and turns through 1 right angle?
(b) from 8 and turns through 2 right angles?
(c) from 10 and turns through 3 right angles?
(d) from 7 and turns through 2 straight angles?
Answer. In 1 complete revolution (clockwise or anti-clockwise), the hour hand of a clock will
rotate by 360∘ or 4 right angles.
(a) the hour hand of a clock starts from 6 and tums through 1 right angle, then it
stop at 9.
Page 9 of 23 Aglasem Schools
Page 11
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
(b) If the hour hand of a Clock Starts from 8 and turns through 2 right angles, then it
will stop at 2.
(c) If the hour hand of a clock starts from 10 and turns through 3 right angles, then
it will stop at 7.
Page : 92 , Block Name : Exercise 5.2
Exercise 5.3
Q1
Answer. (i) Straight angle is of 180∘ and half of a revolution is 180∘ .
Hence, (i) ↔ (c)
(ii) Right angle Is of 90∘ and one-fourth of a revolution Is 190∘ .
Hence, (ii) ↔ (d)
(iii) Acute angles are the angles less than 90∘ . Also, less than one-fourth of a revolution is the
angle less than 90∘ .
Hence, (iii) ↔ (a)
(iv) Obtuse angles are the angles greater than 90∘ but less than 180∘ . Also, between 14 and 12 of
a revolution is the angle whose measure lies between 90∘ and 180∘ .
Hence, (iv) ↔ (e)
(v) Re�ex angles are the angles greater than 180∘ but less than 360∘ . Also, more than half a
revolution is the angle whose measure is greater than 180∘
Hence, (v) ↔ (b)
Page 10 of 23 Aglasem Schools
(b) If the hour hand of a Clock Starts from 8 and turns through 2 right angles, then it
will stop at 2.
(c) If the hour hand of a clock starts from 10 and turns through 3 right angles, then
it will stop at 7.
Page : 92 , Block Name : Exercise 5.2
Exercise 5.3
Q1
Answer. (i) Straight angle is of 180∘ and half of a revolution is 180∘ .
Hence, (i) ↔ (c)
(ii) Right angle Is of 90∘ and one-fourth of a revolution Is 190∘ .
Hence, (ii) ↔ (d)
(iii) Acute angles are the angles less than 90∘ . Also, less than one-fourth of a revolution is the
angle less than 90∘ .
Hence, (iii) ↔ (a)
(iv) Obtuse angles are the angles greater than 90∘ but less than 180∘ . Also, between 14 and 12 of
a revolution is the angle whose measure lies between 90∘ and 180∘ .
Hence, (iv) ↔ (e)
(v) Re�ex angles are the angles greater than 180∘ but less than 360∘ . Also, more than half a
revolution is the angle whose measure is greater than 180∘
Hence, (v) ↔ (b)
Page 10 of 23 Aglasem Schools
Page 12
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
Page : 94 , Block Name : Exercise 5.3
Q2 Classify each one of the following angles as right, straight, acute, obtuse or re�ex:
Answer. (a) Acute angle as its measure is less than 90∘ .
(b) Obtuse angle as its measure iS more than 90∘ but less than 180∘ ,
(c) Right angle as its measure is 90∘ .
(d) Re�ex angle as its measure is more than 180∘ but less than 360∘ .
(e) Straight angle as its measure Is 180∘ .
(f) Acute angle as its measure is less than 90∘ .
Page : 95 , Block Name : Exercise 5.3
Exercise 5.4
Q1 What is the measure of (i) a right angle? (ii) a straight angle?
Answer. (i) The measure of a right angle is 90∘ .
(ii) The measure of a straight angle is 180∘ .
Page : 97 , Block Name : Exercise 5.4
Q2 Say True or False :
(a) The measure of an acute angle < 90∘ .
(b) The measure of an obtuse angle < 90∘ .
(c) The measure of a re�ex angle > 180∘ .
(d) The measure of one complete revolution = 360∘ .
(e) If m m∠A = 53∘ and m∠B = 35∘ , then m∠A > m∠B.
Answer. (a) True
The measure of an acute angle is less than 90∘ .
(b) False
Page 11 of 23 Aglasem Schools
Page : 94 , Block Name : Exercise 5.3
Q2 Classify each one of the following angles as right, straight, acute, obtuse or re�ex:
Answer. (a) Acute angle as its measure is less than 90∘ .
(b) Obtuse angle as its measure iS more than 90∘ but less than 180∘ ,
(c) Right angle as its measure is 90∘ .
(d) Re�ex angle as its measure is more than 180∘ but less than 360∘ .
(e) Straight angle as its measure Is 180∘ .
(f) Acute angle as its measure is less than 90∘ .
Page : 95 , Block Name : Exercise 5.3
Exercise 5.4
Q1 What is the measure of (i) a right angle? (ii) a straight angle?
Answer. (i) The measure of a right angle is 90∘ .
(ii) The measure of a straight angle is 180∘ .
Page : 97 , Block Name : Exercise 5.4
Q2 Say True or False :
(a) The measure of an acute angle < 90∘ .
(b) The measure of an obtuse angle < 90∘ .
(c) The measure of a re�ex angle > 180∘ .
(d) The measure of one complete revolution = 360∘ .
(e) If m m∠A = 53∘ and m∠B = 35∘ , then m∠A > m∠B.
Answer. (a) True
The measure of an acute angle is less than 90∘ .
(b) False
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
The measure of an obtuse angle is greater than 90∘ but less than 180∘ .
(c) True
The measure of a re�ex angle is greater than 180∘ .
(d) True
The measure of one complete revolution is 360∘ .
(e) True
Page : 97 , Block Name : Exercise 5.4
Q3 Write down the measures of
(a) some acute angles.
(b) some obtuse angles.
(give at least two examples of each).
Answer. (a) 45∘ , 70∘
(b) 105∘ , 132∘
Page : 97 , Block Name : Exercise 5.4
Q4 Measure the angles given below using the Protractor and write down the measure.
Answer. (a) 45∘
(b) 120∘
(c) 90∘
(d) 60∘ , 90∘ , and 130∘
Page : 97 , Block Name : Exercise 5.4
Q5 Which angle has a large measure? First estimate and then measure.
Measure of Angle A =
Measure of Angle B =
Page 12 of 23 Aglasem Schools
The measure of an obtuse angle is greater than 90∘ but less than 180∘ .
(c) True
The measure of a re�ex angle is greater than 180∘ .
(d) True
The measure of one complete revolution is 360∘ .
(e) True
Page : 97 , Block Name : Exercise 5.4
Q3 Write down the measures of
(a) some acute angles.
(b) some obtuse angles.
(give at least two examples of each).
Answer. (a) 45∘ , 70∘
(b) 105∘ , 132∘
Page : 97 , Block Name : Exercise 5.4
Q4 Measure the angles given below using the Protractor and write down the measure.
Answer. (a) 45∘
(b) 120∘
(c) 90∘
(d) 60∘ , 90∘ , and 130∘
Page : 97 , Block Name : Exercise 5.4
Q5 Which angle has a large measure? First estimate and then measure.
Measure of Angle A =
Measure of Angle B =
Page 12 of 23 Aglasem Schools
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
Answer. Measure of angle A = 40∘
Measure of angle B = 60∘
∠B has the greater measure than ∠A
Page : 98 , Block Name : Exercise 5.4
Q6 From these two angles which has larger measure? Estimate and then con�rm by measuring
them
Answer. The measures of these angles are 450∘ and 55∘ . Therefore, the angle shown in 2 �gure
is greater.
Page : 98 , Block Name : Exercise 5.4
Q7 Fill in the blanks with acute, obtuse, right or straight : (a) An angle whose measure is less
than that of a right angle is______. (b) An angle whose measure is greater than that of a right
angle is ______. (c) An angle whose measure is the sum of the measures of two right angles is
_____. (d) When the sum of the measures of two angles is that of a right angle, then each one of
them is ______. (e) When the sum of the measures of two angles is that of a straight angle and if
one of them is acute then the other should be _______.
Answer. (a) Acute angle
(b) Obtuse angle (If the angle Is less than 180∘ )
(c) Straight angle
(d) Acute angle
(e) Obtuse angle
Page : 98 , Block Name : Exercise 5.4
Q8 Find the measure of the angle shown in each �gure. (First estimate with your eyes and then
�nd the actual measure with a protractor).
Answer. The measures Of the angles Shown in the above �gure are 40∘ , 130∘ , 65∘ , 135∘
Page 13 of 23 Aglasem Schools
Answer. Measure of angle A = 40∘
Measure of angle B = 60∘
∠B has the greater measure than ∠A
Page : 98 , Block Name : Exercise 5.4
Q6 From these two angles which has larger measure? Estimate and then con�rm by measuring
them
Answer. The measures of these angles are 450∘ and 55∘ . Therefore, the angle shown in 2 �gure
is greater.
Page : 98 , Block Name : Exercise 5.4
Q7 Fill in the blanks with acute, obtuse, right or straight : (a) An angle whose measure is less
than that of a right angle is______. (b) An angle whose measure is greater than that of a right
angle is ______. (c) An angle whose measure is the sum of the measures of two right angles is
_____. (d) When the sum of the measures of two angles is that of a right angle, then each one of
them is ______. (e) When the sum of the measures of two angles is that of a straight angle and if
one of them is acute then the other should be _______.
Answer. (a) Acute angle
(b) Obtuse angle (If the angle Is less than 180∘ )
(c) Straight angle
(d) Acute angle
(e) Obtuse angle
Page : 98 , Block Name : Exercise 5.4
Q8 Find the measure of the angle shown in each �gure. (First estimate with your eyes and then
�nd the actual measure with a protractor).
Answer. The measures Of the angles Shown in the above �gure are 40∘ , 130∘ , 65∘ , 135∘
Page 13 of 23 Aglasem Schools
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
respectively.
Page : 98 , Block Name : Exercise 5.4
Q9 Find the angle measure between the hands of the clock in each �gure :
Answer. (a) 90∘
(b) 30∘
(c) 180∘
Page : 98 , Block Name : Exercise 5.4
Q10 Investigate
In the given �gure, the angle measures 30∘ . Look at the same �gure through a magnifying
glass. Does the angle becomes larger? Does the size of the angle change?
Answer. The measure of this angle will not change.
Page : 99 , Block Name : Exercise 5.4
Q11 Measure and classify each angle :
Answer.
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respectively.
Page : 98 , Block Name : Exercise 5.4
Q9 Find the angle measure between the hands of the clock in each �gure :
Answer. (a) 90∘
(b) 30∘
(c) 180∘
Page : 98 , Block Name : Exercise 5.4
Q10 Investigate
In the given �gure, the angle measures 30∘ . Look at the same �gure through a magnifying
glass. Does the angle becomes larger? Does the size of the angle change?
Answer. The measure of this angle will not change.
Page : 99 , Block Name : Exercise 5.4
Q11 Measure and classify each angle :
Answer.
Page 14 of 23 Aglasem Schools
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
Page : 99 , Block Name : Exercise 5.4
Exercise 5.5
Q1 Which of the following are models for perpendicular lines :
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter ‘L’.
Page 15 of 23 Aglasem Schools
Page : 99 , Block Name : Exercise 5.4
Exercise 5.5
Q1 Which of the following are models for perpendicular lines :
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter ‘L’.
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
(d) The letter V.
Answer. (a) The adjacent edges of a table top are perpendicular to each other.
(b) The lines of a railway track are parallel to each other.
(c) The line segments forming the letter 'L' are perpendicular to each other.
(d) The sides of letter V are Inclined at some acute angle on each other.
Hence, (a) and (c) are the models for perpendicular Iines.
Page : 100 , Block Name : Exercise 5.5
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q2
Let PQ be the perpendicular to the line segment XY . Let PQ and XY intersect
in the point A. What is the measure of ∠PAY ?
Answer.
From the �gure, it can be easily observed that the measure of ∠P AY is 90∘
Page : 100 , Block Name : Exercise 5.5
Q3 There are two set-squares in your box. What are the measures of the angles that are formed
at their corners? Do they have any angle measure that is common?
Answer. One has measure of 90∘ , 45∘ , 45∘
Other has a measure of 90∘ , 30∘ , 60∘
Therefore, the angle 0f 90∘ measure is common between them.
Page : 100 , Block Name : Exercise 5.5
Q4 . Study the diagram. The line l is perpendicular to line m
(a) Is CE = EG?
(b) Does PE bisect CG?
(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) AC > FG
(ii) CD = GH
Page 16 of 23 Aglasem Schools
(d) The letter V.
Answer. (a) The adjacent edges of a table top are perpendicular to each other.
(b) The lines of a railway track are parallel to each other.
(c) The line segments forming the letter 'L' are perpendicular to each other.
(d) The sides of letter V are Inclined at some acute angle on each other.
Hence, (a) and (c) are the models for perpendicular Iines.
Page : 100 , Block Name : Exercise 5.5
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
Q2
Let PQ be the perpendicular to the line segment XY . Let PQ and XY intersect
in the point A. What is the measure of ∠PAY ?
Answer.
From the �gure, it can be easily observed that the measure of ∠P AY is 90∘
Page : 100 , Block Name : Exercise 5.5
Q3 There are two set-squares in your box. What are the measures of the angles that are formed
at their corners? Do they have any angle measure that is common?
Answer. One has measure of 90∘ , 45∘ , 45∘
Other has a measure of 90∘ , 30∘ , 60∘
Therefore, the angle 0f 90∘ measure is common between them.
Page : 100 , Block Name : Exercise 5.5
Q4 . Study the diagram. The line l is perpendicular to line m
(a) Is CE = EG?
(b) Does PE bisect CG?
(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) AC > FG
(ii) CD = GH
Page 16 of 23 Aglasem Schools
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
(iii) BC < EH
Answer. (a) Yes. As CE = EG = 2 units
(b) Yes. PE bisects since CE = EG.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(c) DF and BH
(d) (i) True. As length Of AC and FG of 2 units and I unit respectively.
(ii) True. AS both have 1 unit length.
(ill) True. As the length of BC and EH are of 1 unit and 3 units respectively.
Page : 100 , Block Name : Exercise 5.5
Exercise 5.6
Q1 Name the types of following triangles :
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) △ABC with AB = 8.7cm, AC = 7cm and BC = 6cm
(c) ΔPQR such that PQ = QR = PR = 5cm
(d) ΔDEF with m∠D = 90∘
(e) ΔXYZ with m∠Y = 90∘ and XY = YZ
(f) m∠L = 30∘ , m∠M = 70∘ and m∠N = 80∘ .
Answer. (a) Scalene triangle
(b) Scalene mangle
(c) Equilateral triangle
(d) Right-angled triangle
(e) Right-angled isosceles triangle
(f) Acute angled triangle
Page : 103 , Block Name : Exercise 5.6
Q2 Match the following :
Answer. (i) Equilateral (e)
Page 17 of 23 Aglasem Schools
(iii) BC < EH
Answer. (a) Yes. As CE = EG = 2 units
(b) Yes. PE bisects since CE = EG.
¯¯¯¯¯¯¯¯ ¯¯¯¯¯¯¯¯
(c) DF and BH
(d) (i) True. As length Of AC and FG of 2 units and I unit respectively.
(ii) True. AS both have 1 unit length.
(ill) True. As the length of BC and EH are of 1 unit and 3 units respectively.
Page : 100 , Block Name : Exercise 5.5
Exercise 5.6
Q1 Name the types of following triangles :
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) △ABC with AB = 8.7cm, AC = 7cm and BC = 6cm
(c) ΔPQR such that PQ = QR = PR = 5cm
(d) ΔDEF with m∠D = 90∘
(e) ΔXYZ with m∠Y = 90∘ and XY = YZ
(f) m∠L = 30∘ , m∠M = 70∘ and m∠N = 80∘ .
Answer. (a) Scalene triangle
(b) Scalene mangle
(c) Equilateral triangle
(d) Right-angled triangle
(e) Right-angled isosceles triangle
(f) Acute angled triangle
Page : 103 , Block Name : Exercise 5.6
Q2 Match the following :
Answer. (i) Equilateral (e)
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
(ii) Isosceles (g)
(m) scalene (a)
(v) Right-angled (d)
(vi) Obtuse-angled (c)
(vii) Isosceles right-angled (b)
Page : 103 , Block Name : Exercise 5.6
Q3 Name each of the following triangles in two different ways: (you may judge the nature of the
angle by observation)
Answer. (a) Acute angled and isosceles
(b) Right-angled and scalene
(c) Obtuse-angled and isosceles
(d) Right-angled and isosceles
(e) Acute-angled and equilateral
(f) Obtuse-angled and scalene
Page : 103 , Block Name : Exercise 5.6
Q4 Try to construct triangles using match sticks. Some are shown here.Can you make a triangle
with
(a) 3 matchsticks?
(b) 4 matchsticks?
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(ii) Isosceles (g)
(m) scalene (a)
(v) Right-angled (d)
(vi) Obtuse-angled (c)
(vii) Isosceles right-angled (b)
Page : 103 , Block Name : Exercise 5.6
Q3 Name each of the following triangles in two different ways: (you may judge the nature of the
angle by observation)
Answer. (a) Acute angled and isosceles
(b) Right-angled and scalene
(c) Obtuse-angled and isosceles
(d) Right-angled and isosceles
(e) Acute-angled and equilateral
(f) Obtuse-angled and scalene
Page : 103 , Block Name : Exercise 5.6
Q4 Try to construct triangles using match sticks. Some are shown here.Can you make a triangle
with
(a) 3 matchsticks?
(b) 4 matchsticks?
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
(c) 5 matchsticks?
(d) 6 matchsticks?
(Remember you have to use all the available matchsticks in each case) Name the type of
triangle in each case. If you cannot make a triangle, think of reasons for it.
Answer. (a) By using 3 matchsticks, we can form a triangle as
(b) By using 4 matchsticks, we cannot form a triangle. This is because the sum of the
lengths of any two sides of a triangle is always greater than the length of the remaining
side of the triangle.
(c) By using 5 matchsticks, we can form a triangle as
(d) using 6 matchsticks, we can form a triangle as
Page : 103 , Block Name : Exercise 5.6
Exercise 5.7
Q1 1. Say True or False : (a) Each angle of a rectangle is a right angle. (b) The opposite sides of a
rectangle are equal in length. (c) The diagonals of a square are perpendicular to one another. (d)
All the sides of a rhombus are of equal length. (e) All the sides of a parallelogram are of equal
length. (f) The opposite sides of a trapezium are parallel.
Answer. (a) True
(b) True
(c) True
(d) True
(e) False
(f) False
Page : 106 , Block Name : Exercise 5.7
Q2 Give reasons for the following :
(a) A square can be thought of as a special rectangle.
(b) A rectangle can be thought of as a special parallelogram.
(c) A square can be thought of as a special rhombus.
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(c) 5 matchsticks?
(d) 6 matchsticks?
(Remember you have to use all the available matchsticks in each case) Name the type of
triangle in each case. If you cannot make a triangle, think of reasons for it.
Answer. (a) By using 3 matchsticks, we can form a triangle as
(b) By using 4 matchsticks, we cannot form a triangle. This is because the sum of the
lengths of any two sides of a triangle is always greater than the length of the remaining
side of the triangle.
(c) By using 5 matchsticks, we can form a triangle as
(d) using 6 matchsticks, we can form a triangle as
Page : 103 , Block Name : Exercise 5.6
Exercise 5.7
Q1 1. Say True or False : (a) Each angle of a rectangle is a right angle. (b) The opposite sides of a
rectangle are equal in length. (c) The diagonals of a square are perpendicular to one another. (d)
All the sides of a rhombus are of equal length. (e) All the sides of a parallelogram are of equal
length. (f) The opposite sides of a trapezium are parallel.
Answer. (a) True
(b) True
(c) True
(d) True
(e) False
(f) False
Page : 106 , Block Name : Exercise 5.7
Q2 Give reasons for the following :
(a) A square can be thought of as a special rectangle.
(b) A rectangle can be thought of as a special parallelogram.
(c) A square can be thought of as a special rhombus.
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
(d) Squares, rectangles, parallelograms are all quadrilaterals.
(e) Square is also a parallelogram.
Answer. (a) In a rectangle, all the interior angles are of the same measure, I.e., 90∘ and only
the opposite sides of the rectangle are of the same length whereas In case of a square,
all the angles are Of 90∘ and all the Sides are Of the same length. In Other words,
a rectangle with all sides equal becomes a square. Therefore, a square is a special
rectangle.
(b) Opposite sides of a parallelogram are parallel and equal. In a rectangle, the opposite
sides are parallel and equal. Also, all the interior angles of the rectangle are of the same
measure, i.e., 90∘ . In other words, a parallelogram with each angle a right angle
becomes a rectangle. Therefore, a rectangle can be thought of as a special
parallelogram.
(c) All sides of a rhombus and a square are equal . However, in case of a square, all
interior angles of 90∘ measure. A rhombus with each angle a right angle becomes a
square. Therefore, a square can be thought of as a special rhombus,
(d) All are closed �gures made of 4 line segments, Therefore, all these are
quadrilaterals.
(e) Opposite sides of a parallelogram are parallel and equal. In a square, the opposite
are parallel and the lengths of all the four sides equal. Therefore, a square can
be thought of as a special parallelogram.
Page : 106 , Block Name : Exercise 5.7
Q3 A �gure is said to be regular if its sides are equal in length and angles are equal in measure.
Can you identify the regular quadrilateral?
Answer. In a square, all the interior angles are of 90∘ and all the sides are of the same length.
Therefore, a square is a regular quadrilateral.
Page : 106 , Block Name : Exercise 5.7
Exercise 5.8
Q1 Examine whether the following are polygons. If any one among them is not, say why?
Answer. (a) tt Is not a polygon as It Is not a closed �gure.
(b) Yes, it is a polygon made of 6 sides.
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(d) Squares, rectangles, parallelograms are all quadrilaterals.
(e) Square is also a parallelogram.
Answer. (a) In a rectangle, all the interior angles are of the same measure, I.e., 90∘ and only
the opposite sides of the rectangle are of the same length whereas In case of a square,
all the angles are Of 90∘ and all the Sides are Of the same length. In Other words,
a rectangle with all sides equal becomes a square. Therefore, a square is a special
rectangle.
(b) Opposite sides of a parallelogram are parallel and equal. In a rectangle, the opposite
sides are parallel and equal. Also, all the interior angles of the rectangle are of the same
measure, i.e., 90∘ . In other words, a parallelogram with each angle a right angle
becomes a rectangle. Therefore, a rectangle can be thought of as a special
parallelogram.
(c) All sides of a rhombus and a square are equal . However, in case of a square, all
interior angles of 90∘ measure. A rhombus with each angle a right angle becomes a
square. Therefore, a square can be thought of as a special rhombus,
(d) All are closed �gures made of 4 line segments, Therefore, all these are
quadrilaterals.
(e) Opposite sides of a parallelogram are parallel and equal. In a square, the opposite
are parallel and the lengths of all the four sides equal. Therefore, a square can
be thought of as a special parallelogram.
Page : 106 , Block Name : Exercise 5.7
Q3 A �gure is said to be regular if its sides are equal in length and angles are equal in measure.
Can you identify the regular quadrilateral?
Answer. In a square, all the interior angles are of 90∘ and all the sides are of the same length.
Therefore, a square is a regular quadrilateral.
Page : 106 , Block Name : Exercise 5.7
Exercise 5.8
Q1 Examine whether the following are polygons. If any one among them is not, say why?
Answer. (a) tt Is not a polygon as It Is not a closed �gure.
(b) Yes, it is a polygon made of 6 sides.
Page 20 of 23 Aglasem Schools
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
(c) No, it is not made of line segments.
(d) No, it is not made of only line segments.
Page : 108 , Block Name : Exercise 5.8
Q2 Name each polygon.
Make two more examples of each of these.
Answer. (a) The given �gure is a quadrilateral as this closed �gure is made of 4
line segments. Two more examples are
(b) The given �gure is a triangle as this dosed �gure Is made of 3 line segments. Two
more are
(c) The given �gure iS a pentagon as this Closed �gure iS made of 5 line segments. Two more
examples are
(d) The given �gure is an octagon as this closed �gure is made of 8 line segments. Two
more examples are
Page : 108 . Block Name : Exercise 5.8
Q3 Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a
triangle. Identify the type of the triangle you have drawn.
Answer. An isosceles triangle by joining three of the vertices of a hexagon can be drawn as
follows.
Page 21 of 23 Aglasem Schools
(c) No, it is not made of line segments.
(d) No, it is not made of only line segments.
Page : 108 , Block Name : Exercise 5.8
Q2 Name each polygon.
Make two more examples of each of these.
Answer. (a) The given �gure is a quadrilateral as this closed �gure is made of 4
line segments. Two more examples are
(b) The given �gure is a triangle as this dosed �gure Is made of 3 line segments. Two
more are
(c) The given �gure iS a pentagon as this Closed �gure iS made of 5 line segments. Two more
examples are
(d) The given �gure is an octagon as this closed �gure is made of 8 line segments. Two
more examples are
Page : 108 . Block Name : Exercise 5.8
Q3 Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a
triangle. Identify the type of the triangle you have drawn.
Answer. An isosceles triangle by joining three of the vertices of a hexagon can be drawn as
follows.
Page 21 of 23 Aglasem Schools
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Book: Mathematics NCERT Solutions | Chapter - 5 Maths
Page : 108 . Block Name : Exercise 5.8
Q4 Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle
by joining exactly four of the vertices of the octagon.
Answer.
Page : 108 . Block Name : Exercise 5.8
Q5 A diagonal is a line segment that joins any two vertices of the polygon and is not a side of
the polygon. Draw a rough sketch of a pentagon and draw its diagonals.
Answer. It can be observed here that AC, AD, BO, BE, CE are the diagonals.
Page : 108 . Block Name : Exercise 5.8
Exercise 5.9
Q1 Match the following :
Page 22 of 23 Aglasem Schools
Page : 108 . Block Name : Exercise 5.8
Q4 Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle
by joining exactly four of the vertices of the octagon.
Answer.
Page : 108 . Block Name : Exercise 5.8
Q5 A diagonal is a line segment that joins any two vertices of the polygon and is not a side of
the polygon. Draw a rough sketch of a pentagon and draw its diagonals.
Answer. It can be observed here that AC, AD, BO, BE, CE are the diagonals.
Page : 108 . Block Name : Exercise 5.8
Exercise 5.9
Q1 Match the following :
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Page 24
Book: Mathematics NCERT Solutions | Chapter - 5 Maths
Give two new examples of each shape.
Answer. (a) (ii)
(b) (iv)
(c) (v)
(d) (iii)
(e) (i)
Page : 111 . Block Name : Exercise 5.9
Q2 What shape is
(a) Your instrument box? (b) A brick? (c) A match box? (d) A road-roller? (e) A sweet laddu?
Answer. (a) Cuboid
(b) cuboid
(c) Cuboid
(d) Cylinder
(e) sphere
Page : 111 . Block Name : Exercise 5.9
Page 23 of 23 Aglasem Schools
Give two new examples of each shape.
Answer. (a) (ii)
(b) (iv)
(c) (v)
(d) (iii)
(e) (i)
Page : 111 . Block Name : Exercise 5.9
Q2 What shape is
(a) Your instrument box? (b) A brick? (c) A match box? (d) A road-roller? (e) A sweet laddu?
Answer. (a) Cuboid
(b) cuboid
(c) Cuboid
(d) Cylinder
(e) sphere
Page : 111 . Block Name : Exercise 5.9
Page 23 of 23 Aglasem Schools
Document Details
| Board / Org | NCERT |
| Exam | Class 6 |
| Type | Solution |
| Pages | 24 |
| Updated | 22 Jul 2026 |