Class 7 Maths Notes for Line And Angles
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Page 1
NOTES
CLASS 7
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CLASS 7
MATHS
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Page 2
LINE AND ANGLES
INTRODUCTION – In earlier classes we have learnt about lines, line segments, rays,
angles, acute, obtuse, right and reflex angles. We shall learn about complementary
angles, supplementary angles, pair of lines, intersecting lines, parallel lines and
transversal.
We shall also learn about angle made by a transversal with parallel lines & non-parallel
lines
Complementary Angles: When the sum of the measures of two angles is 90°, the angles
are complementary angles. Each angle is said to be complement of the other angle.
Supplementary Angles: When the sum of the measures of two angles is 180°, then the
angles are supplementary angles. Each angle is said to be supplement of the other angle.
Angles made by Transversal to Two Parallel Lines
Property 1: Pairs of alternate (interior/exterior) angles are equal.
Alternate Interior Angles: ∠3 = ∠6 ∠ 4= ∠5
Alternate Exterior Angles: ∠1 = ∠8 ∠2 = ∠7
Property 2: Pairs of Corresponding Angles are equal.
∠1 = ∠6 ∠2 = ∠5 ∠3 = ∠8 ∠4 = ∠7
Property 3: The sum of the interior angles on the same side
of the transversal is 180° or Supplementary.
∠3 + ∠5 = ∠4 + ∠6 = 180°
II SOME EXAMPLES WITH SOLUTIONS:
M.C.Q
1. The angles between North and West and South and East are
(a) complementary (b) supplementary
(c) both are acute (d) both are obtuse
Answer: From the above figure, it is clear that the angle
between North and West is 90° and
South and East is 90°.
∴ Sum of these two angles = 90° + 90° = 180°
Hence, the two angles are supplementary, as their sum is 180°.
2. If the complement of an angle is 79°, then the angle will be of
(a) 1° (b) 11°
(c) 79° (d) 101°
Answer: (b) Let the angle be x°. Then, the complement of x will be (90 – x)°.
Given, complement of x° is 79°.
∴ (90 – x)°= 79°
⇒ x° = 90° – 79°= 11°
Therefore, the required angle is 11°.
Note Sum of the complementary angles is 90°.
43
INTRODUCTION – In earlier classes we have learnt about lines, line segments, rays,
angles, acute, obtuse, right and reflex angles. We shall learn about complementary
angles, supplementary angles, pair of lines, intersecting lines, parallel lines and
transversal.
We shall also learn about angle made by a transversal with parallel lines & non-parallel
lines
Complementary Angles: When the sum of the measures of two angles is 90°, the angles
are complementary angles. Each angle is said to be complement of the other angle.
Supplementary Angles: When the sum of the measures of two angles is 180°, then the
angles are supplementary angles. Each angle is said to be supplement of the other angle.
Angles made by Transversal to Two Parallel Lines
Property 1: Pairs of alternate (interior/exterior) angles are equal.
Alternate Interior Angles: ∠3 = ∠6 ∠ 4= ∠5
Alternate Exterior Angles: ∠1 = ∠8 ∠2 = ∠7
Property 2: Pairs of Corresponding Angles are equal.
∠1 = ∠6 ∠2 = ∠5 ∠3 = ∠8 ∠4 = ∠7
Property 3: The sum of the interior angles on the same side
of the transversal is 180° or Supplementary.
∠3 + ∠5 = ∠4 + ∠6 = 180°
II SOME EXAMPLES WITH SOLUTIONS:
M.C.Q
1. The angles between North and West and South and East are
(a) complementary (b) supplementary
(c) both are acute (d) both are obtuse
Answer: From the above figure, it is clear that the angle
between North and West is 90° and
South and East is 90°.
∴ Sum of these two angles = 90° + 90° = 180°
Hence, the two angles are supplementary, as their sum is 180°.
2. If the complement of an angle is 79°, then the angle will be of
(a) 1° (b) 11°
(c) 79° (d) 101°
Answer: (b) Let the angle be x°. Then, the complement of x will be (90 – x)°.
Given, complement of x° is 79°.
∴ (90 – x)°= 79°
⇒ x° = 90° – 79°= 11°
Therefore, the required angle is 11°.
Note Sum of the complementary angles is 90°.
43
Page 3
3. The angles x – 10° and 190° – x are
(a) interior angles on the same side of the transversal
(b) making a linear pair
(c) complementary
(d) supplementary
Answer:(d) Sum of the given angles
= (x – 10°)+ (190° – x)= x -10° + 190° – x
= (x-x) + (190°-10°)=0 + 180°= 180°
Since, the sum of given angles is 180°, Hence, they are supplementary.
4. In the given figure, PQ || RS and a : b =3 : 2. Then, f is equal to
Answer: (b) We have, a:b = 3:2
Let a = 3x and b=2x
Since, a and b form a linear pair.
Short-Answer Type Questions:
1. If two supplementary angles have equal measures. What is the measure of each
angle? Ans : 900,900
2. If two complementary angles have equal measures. What is the measure of each
angle? Ans : 450,450
3. If two supplementary angles in the ratio of 1:2. Find the angles.
Ans : 600,1200
44
(a) interior angles on the same side of the transversal
(b) making a linear pair
(c) complementary
(d) supplementary
Answer:(d) Sum of the given angles
= (x – 10°)+ (190° – x)= x -10° + 190° – x
= (x-x) + (190°-10°)=0 + 180°= 180°
Since, the sum of given angles is 180°, Hence, they are supplementary.
4. In the given figure, PQ || RS and a : b =3 : 2. Then, f is equal to
Answer: (b) We have, a:b = 3:2
Let a = 3x and b=2x
Since, a and b form a linear pair.
Short-Answer Type Questions:
1. If two supplementary angles have equal measures. What is the measure of each
angle? Ans : 900,900
2. If two complementary angles have equal measures. What is the measure of each
angle? Ans : 450,450
3. If two supplementary angles in the ratio of 1:2. Find the angles.
Ans : 600,1200
44
Page 4
Long-Answer Type Questions:
1. In the given figure, PQ || RS. If ∠1 = (2a + b)° and ∠6 = (3a – b)° ,
then the measure of ∠2 in terms of b is
Solution:
2. In the given figure, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. Find ∠ABC and
∠CDE.
Solution:
Since, BD||AE and CG is transversal.
45
1. In the given figure, PQ || RS. If ∠1 = (2a + b)° and ∠6 = (3a – b)° ,
then the measure of ∠2 in terms of b is
Solution:
2. In the given figure, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. Find ∠ABC and
∠CDE.
Solution:
Since, BD||AE and CG is transversal.
45
Page 5
Case Study Based
1. The drawings below (figure), show angles formed by the goalposts at different positions
of a football player. The greater the angle, the better chance the player has of scoring a
goal. e.g. The player has a better chance of scoring a goal from position A than from
position B.
In parts (a) and (b) given below, it may help to trace the diagrams and draw and measure
angles.
(a) Seven football players are practicing their kicks. They are lined up in a straight line
infront of the goalpost [figure (ii)]. Which player has the best (the greatest) kicking angle?
(b) Now the players are lined up as shown in figure (iii). Which player has the best kicking
angle?
(c) Estimate atleast two situations, such that the angles formed by different positions of two
players are complement to each other.
Solution:
From the above figure, we can say that player 4 has the best kicking angle, as it is
greatest.
(c) Since, the angles are complementary. Hence, two situations are 45°, 45° and 30°, 60°.
46
1. The drawings below (figure), show angles formed by the goalposts at different positions
of a football player. The greater the angle, the better chance the player has of scoring a
goal. e.g. The player has a better chance of scoring a goal from position A than from
position B.
In parts (a) and (b) given below, it may help to trace the diagrams and draw and measure
angles.
(a) Seven football players are practicing their kicks. They are lined up in a straight line
infront of the goalpost [figure (ii)]. Which player has the best (the greatest) kicking angle?
(b) Now the players are lined up as shown in figure (iii). Which player has the best kicking
angle?
(c) Estimate atleast two situations, such that the angles formed by different positions of two
players are complement to each other.
Solution:
From the above figure, we can say that player 4 has the best kicking angle, as it is
greatest.
(c) Since, the angles are complementary. Hence, two situations are 45°, 45° and 30°, 60°.
46
Page 6
III Questions For Practice
MCQ Based Questions:
1. In the given figure, if QP|| SR, the value of a is
2. The angles x – 10° and 190° – x are
(a) interior angles on the same side of the transversal
(b) making a linear pair
(c) complementary
(d) supplementary
3. The angles x and 90°- x are
(a) supplementary (b) complementary
(c) vertically opposite (d) making a linear pair
4. If the complement of an angle is 79°, then the angle will be of
(a) 1° (b) 11°
(c) 79° (d) 101°
5. Angles between South and West and South and East are
(a) vertically opposite angles (b) complementary angles
(c) making a linear pair (d) adjacent but not supplementary
6. In the given figure, PQ || RS and a : b =3 : 2. Then, f is equal to
47
MCQ Based Questions:
1. In the given figure, if QP|| SR, the value of a is
2. The angles x – 10° and 190° – x are
(a) interior angles on the same side of the transversal
(b) making a linear pair
(c) complementary
(d) supplementary
3. The angles x and 90°- x are
(a) supplementary (b) complementary
(c) vertically opposite (d) making a linear pair
4. If the complement of an angle is 79°, then the angle will be of
(a) 1° (b) 11°
(c) 79° (d) 101°
5. Angles between South and West and South and East are
(a) vertically opposite angles (b) complementary angles
(c) making a linear pair (d) adjacent but not supplementary
6. In the given figure, PQ || RS and a : b =3 : 2. Then, f is equal to
47
Page 7
7. In the given figure, line l intersects two parallel lines PQ and RS. Then, which one of
the following is not true?
8. In the above figure (Q. No. 7), which one of the following is not true?
(a) ∠1+ ∠5=180° (b) ∠2 + ∠5=180°
(c) ∠3 + ∠8=180° (d) ∠2 + ∠3=180°
9. In the above figure (Q.No. 7), which of the following is true?
(a) ∠1 = ∠5 (b) ∠4 = ∠8 (c) ∠5 = ∠8 (d) ∠3 = ∠7
10. In the given figure, if PQ || RS and QR || TS, then the value of a is
Short Answer Type Questions
1. Can two acute angles be complement to each other?
2. Can two obtuse angles be complement to each other?
3. Can two right angles be complement to each other?
4. The difference in the measures of two complementary angles is 120. Find the
measures of the angles?
5. Find at least two examples from your surroundings where lines intersect at right
angles?
6. Suppose two lines are given. How many transversals can you draw for these lines?
7. If a line is transversal to three lines, how many points of intersection are there?
8. If two lines intersect, do they always intersects at right angles?
9. Find the value of x in each of the following figures if l || m.
10. What will be the measure of the supplement of the angle 1690
48
the following is not true?
8. In the above figure (Q. No. 7), which one of the following is not true?
(a) ∠1+ ∠5=180° (b) ∠2 + ∠5=180°
(c) ∠3 + ∠8=180° (d) ∠2 + ∠3=180°
9. In the above figure (Q.No. 7), which of the following is true?
(a) ∠1 = ∠5 (b) ∠4 = ∠8 (c) ∠5 = ∠8 (d) ∠3 = ∠7
10. In the given figure, if PQ || RS and QR || TS, then the value of a is
Short Answer Type Questions
1. Can two acute angles be complement to each other?
2. Can two obtuse angles be complement to each other?
3. Can two right angles be complement to each other?
4. The difference in the measures of two complementary angles is 120. Find the
measures of the angles?
5. Find at least two examples from your surroundings where lines intersect at right
angles?
6. Suppose two lines are given. How many transversals can you draw for these lines?
7. If a line is transversal to three lines, how many points of intersection are there?
8. If two lines intersect, do they always intersects at right angles?
9. Find the value of x in each of the following figures if l || m.
10. What will be the measure of the supplement of the angle 1690
48
Page 8
Long Answer Type Questions
1. In the adjoining figure, p || q. Find the unknown angles.
2. Draw any rectangle and find the measures of angles at the four vertices made by the
intersecting lines.
3. l ∥ m and p ∥ q. Find the values of x, y, z, t.
4. Among two supplementary angles, the measures of the larger angle is 440 more than
the measure of the smaller. Find their measures?
5. State the property that is used in each of the following statements?
(i) If a || b, then ∠1 = ∠5.
(ii) If ∠4 = ∠6, then a || b.
(iii) If ∠4 + ∠5 = 180°, then a || b.
6. In the adjoining figure, identify
(i) the pairs of corresponding angles.
(ii) the pairs of alternate interior angles.
(iii) the pairs of interior angles on the same side of the transversal
49
1. In the adjoining figure, p || q. Find the unknown angles.
2. Draw any rectangle and find the measures of angles at the four vertices made by the
intersecting lines.
3. l ∥ m and p ∥ q. Find the values of x, y, z, t.
4. Among two supplementary angles, the measures of the larger angle is 440 more than
the measure of the smaller. Find their measures?
5. State the property that is used in each of the following statements?
(i) If a || b, then ∠1 = ∠5.
(ii) If ∠4 = ∠6, then a || b.
(iii) If ∠4 + ∠5 = 180°, then a || b.
6. In the adjoining figure, identify
(i) the pairs of corresponding angles.
(ii) the pairs of alternate interior angles.
(iii) the pairs of interior angles on the same side of the transversal
49
Page 9
Case Study Based Questions
1. The legs of a stool make an angle of 35° with the floor, as shown in the given figure. Answer
the following questions :
(i) Find the angle value of x.
(ii) Find the angle value of y.
2.Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a || d, b || e and c
|| f. Chhaya marks an angle as 120° as shown in the given figure and Amisha to find the
(i) Value of x
(ii) Value of y
(iii) Value of z
ANSWERS :
III Questions For Practice
MCQ Based Questions: Answers
1 (c) 2 (d) 3 (b) 4 (b) 5 (c) 6 (b) 7 (d) 8 (d) 9 (c) 10 (a)
Short Answer Type Questions
50
1. The legs of a stool make an angle of 35° with the floor, as shown in the given figure. Answer
the following questions :
(i) Find the angle value of x.
(ii) Find the angle value of y.
2.Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a || d, b || e and c
|| f. Chhaya marks an angle as 120° as shown in the given figure and Amisha to find the
(i) Value of x
(ii) Value of y
(iii) Value of z
ANSWERS :
III Questions For Practice
MCQ Based Questions: Answers
1 (c) 2 (d) 3 (b) 4 (b) 5 (c) 6 (b) 7 (d) 8 (d) 9 (c) 10 (a)
Short Answer Type Questions
50
Page 10
1 Yes 2 No 3 No 4 510& 390 5 Student Desk, Edges of geometry box
6 Infinite 7 Three points of intersection 8 No 9 600 10 110
Long Answer Type Questions
1 a = 550, b = 1250, c = 550, d = 1250, e = 550, f = 550
2 Each angle is 9003 x = y = z = t = 8004 680, 1120
5 (i) Yes, Pair of corresponding angles
(ii) Yes, If pair of alternate interior angles are equal then the lines are parallel.
(iii)Yes, If the angle sum on the same side of the transversal is 1800 then the lines are
parallel.
6 (i) ∠ 1&∠ 5, ∠ 4&∠ 8, ∠ 3 &∠ 7, ∠ 2 &∠ 6 (ii) ∠ 3&∠ 5, ∠ 2 &∠ 8,
(iii) ∠ 2&∠ 5, ∠ 3&∠ 8,
Case Study Based Questions
1 (i) x = 350 (ii) Y = 14502 (i) x = 600 (ii) Y = 1450 (iii) Z = 600
CHAPTER TEST 1- LINES AND ANGLES
Time : 30 min Class : VII M.M:20
SECTION – A (1 × 4 = 4)
1. The measure of supplement of the angle 135° is
(a) 47° (b) 45° (c) 90° (d) 55°
2. The measure of complement of the angle 89° is
(a) 11° (b) 10° (c) 1° (d) 2°
3. If two lines are parallel and a transversal intersect to them then each pair of
corresponding angles are
(a) 90° (b) 180° (c) equal (d) none of these
4. If two supplementary angles are in the ratio3 : 7. Then the smaller angle value is
(a) 126° (b) 18° (c) 54° (d) 10°
SECTION – B (2 × 3 = 6)
5. Find the angle which is equal to its compliment.
6. Find the angle which is equal to its supplement.
7. If a transversal intersects two lines at distinct points then how many pairs of alternate
exterior angles formed.
SECTION – C (3 × 2 = 6)
8. An angle is equal to five times its complement. Determine its measure.
9. In figure linem⃦ n and ∠1 = 65°. Find ∠5 and ∠8.
51
6 Infinite 7 Three points of intersection 8 No 9 600 10 110
Long Answer Type Questions
1 a = 550, b = 1250, c = 550, d = 1250, e = 550, f = 550
2 Each angle is 9003 x = y = z = t = 8004 680, 1120
5 (i) Yes, Pair of corresponding angles
(ii) Yes, If pair of alternate interior angles are equal then the lines are parallel.
(iii)Yes, If the angle sum on the same side of the transversal is 1800 then the lines are
parallel.
6 (i) ∠ 1&∠ 5, ∠ 4&∠ 8, ∠ 3 &∠ 7, ∠ 2 &∠ 6 (ii) ∠ 3&∠ 5, ∠ 2 &∠ 8,
(iii) ∠ 2&∠ 5, ∠ 3&∠ 8,
Case Study Based Questions
1 (i) x = 350 (ii) Y = 14502 (i) x = 600 (ii) Y = 1450 (iii) Z = 600
CHAPTER TEST 1- LINES AND ANGLES
Time : 30 min Class : VII M.M:20
SECTION – A (1 × 4 = 4)
1. The measure of supplement of the angle 135° is
(a) 47° (b) 45° (c) 90° (d) 55°
2. The measure of complement of the angle 89° is
(a) 11° (b) 10° (c) 1° (d) 2°
3. If two lines are parallel and a transversal intersect to them then each pair of
corresponding angles are
(a) 90° (b) 180° (c) equal (d) none of these
4. If two supplementary angles are in the ratio3 : 7. Then the smaller angle value is
(a) 126° (b) 18° (c) 54° (d) 10°
SECTION – B (2 × 3 = 6)
5. Find the angle which is equal to its compliment.
6. Find the angle which is equal to its supplement.
7. If a transversal intersects two lines at distinct points then how many pairs of alternate
exterior angles formed.
SECTION – C (3 × 2 = 6)
8. An angle is equal to five times its complement. Determine its measure.
9. In figure linem⃦ n and ∠1 = 65°. Find ∠5 and ∠8.
51
Page 11
SECTION – D (4 × 1 = 4)
10. In figure line l⃦ m. Find the values of a, b, c, d. Give reasons
CHAPTER TEST 2- LINES AND ANGLES
Time : 45 min M.M:30
SECTION – A (1 × 6 = 6)
1. Find the measure of the angle which is double of its complementary angle?
(a) 60° (b) 30° (c) 45° (d) 120°
2. Find the measure of the angle which is half of its supplementary angle?
(a) 60° (b) 120° (c) 90° (d) 45°
3. The measure of the supplement of the angle 179° is
(a) 1° (b) 2° (c) 3° (d) 4°
4. The measure of the compliment of the angle 10° is
(a) 20° (b) 40° (c) 60° (d) 70°
5. In the following figure, which pair of angles are not the corresponding angles
(a) ∠1, ∠5 (b) ∠3, ∠7 (c) ∠2, ∠6 (d) ∠3, ∠5
6. In the above figure which pair of angles are alternate interior angles?
(a) ∠1, ∠5 (b) ∠2, ∠6 (c) ∠3, ∠7 (d) ∠3, ∠5
SECTION – B (2 × 5 = 10)
7. If two supplementary angles have equal measures. what is the measure of each angle.
8. If two complementary angles have equal measures what is the measure of each angle.
9. An angle is equal to four times its compliment. Determine its measure.
10. Line l ⃦ line m, n is a transversal and ∠1 = 40°. Find all the other angles form between
transversal and lines.
52
10. In figure line l⃦ m. Find the values of a, b, c, d. Give reasons
CHAPTER TEST 2- LINES AND ANGLES
Time : 45 min M.M:30
SECTION – A (1 × 6 = 6)
1. Find the measure of the angle which is double of its complementary angle?
(a) 60° (b) 30° (c) 45° (d) 120°
2. Find the measure of the angle which is half of its supplementary angle?
(a) 60° (b) 120° (c) 90° (d) 45°
3. The measure of the supplement of the angle 179° is
(a) 1° (b) 2° (c) 3° (d) 4°
4. The measure of the compliment of the angle 10° is
(a) 20° (b) 40° (c) 60° (d) 70°
5. In the following figure, which pair of angles are not the corresponding angles
(a) ∠1, ∠5 (b) ∠3, ∠7 (c) ∠2, ∠6 (d) ∠3, ∠5
6. In the above figure which pair of angles are alternate interior angles?
(a) ∠1, ∠5 (b) ∠2, ∠6 (c) ∠3, ∠7 (d) ∠3, ∠5
SECTION – B (2 × 5 = 10)
7. If two supplementary angles have equal measures. what is the measure of each angle.
8. If two complementary angles have equal measures what is the measure of each angle.
9. An angle is equal to four times its compliment. Determine its measure.
10. Line l ⃦ line m, n is a transversal and ∠1 = 40°. Find all the other angles form between
transversal and lines.
52
Page 12
11. Measures (in degree) of two supplementary angles are consecutive odd integers, Find the
angles value.
SECTION – C (3 × 3 = 9)
12. Find the measure of an angle which is compliment of itself.
13. Two supplementary angles differ by 34°. Find the angles.
14. In fig., the corresponding arms of ∠ABC and ∠DEF are parallel. If ∠ABC = 75°, find ∠
DEF.
SECTION – D (2 + 1 + 2)
15. A road crosses a railway line at an angle of 30°as shown in figure
(i) Find the value of a.
(ii) Find the value of b
(iii) Find the value of c
53
angles value.
SECTION – C (3 × 3 = 9)
12. Find the measure of an angle which is compliment of itself.
13. Two supplementary angles differ by 34°. Find the angles.
14. In fig., the corresponding arms of ∠ABC and ∠DEF are parallel. If ∠ABC = 75°, find ∠
DEF.
SECTION – D (2 + 1 + 2)
15. A road crosses a railway line at an angle of 30°as shown in figure
(i) Find the value of a.
(ii) Find the value of b
(iii) Find the value of c
53
Page 13
Study Materials
Notes
Model Papers Class 6 Notes
Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes
Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats
Maps of India / World Class 12 Notes
Books and Solutions
NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions
Notes
Model Papers Class 6 Notes
Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes
Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats
Maps of India / World Class 12 Notes
Books and Solutions
NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions
Document Details
| Board / Org | Aglasem |
| Exam | Class 7 |
| Type | Notes |
| Pages | 13 |
| Language | english |
| Updated | 24 Sep 2026 |