NCERT Solutions Class 5 Maths Chapter 3 Angles As Turns

F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T

C L A S S 5 · M AT H S

NCERT Solutions

Chapter 3: Angles as Turns

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

32 – 41 10 46 English

Solutions, notes, sample papers & more at 101 pages

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

CLASS 5 · MATHS · MATH MELA

NCERT Solutions — Chapter 3: Angles as Turns
Chapter 3 of Math Mela begins with a game of “Statue”. When you spin round and stop, you have made a turn
— and this chapter measures how much of a turn it was. A quarter turn, a half turn, a three-quarter turn, a
full turn; a right angle, an acute angle, an obtuse angle, a straight angle; and the two directions of turning —
clockwise and anti-clockwise.

TEXTBOOK BOOK PAGES

Math Mela (Class 5) 32 – 41

SECTIONS QUESTIONS

10 46

MEDIUM

English

In-text Questions — Page 32
Let us play “Statue”

DISCUSS IN CLASS

Q1 Can you recognise the child in the picture who has made a full turn? Who has made
a half turn? How do you know? Discuss in class.

Before — everyone is facing you STATUE! — everyone has stopped

A B C D A B C D

The class plays “Statue”. In the first picture A, B, C and D are all facing you. In the second
picture the teacher has called “STATUE!” and each child has stopped part-way through a
turn — look at which way each one is facing now.

ANSWER

B and C have made a full turn. A has made a half turn. D has made a quarter turn.
Here is how to read the two pictures.

1. In the first picture, all four children — A, B, C and D — are facing us.
2. Then the teacher says “STATUE!” and everyone stops.

Page 1 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

3. Now look at each child again and ask: which way is this child facing now?

CHILD FACING AT FIRST FACING AFTER “STATUE” TURN MADE

A towards us away from us (we see his back) half turn

B towards us towards us again full turn

C towards us towards us again full turn

D towards us sideways quarter turn

At first

A B C D

After “Statue!”

A B C D

The arrow shows which way the child is facing (seen from above).

Seen from above. A is now facing the opposite way — that is a half turn. B and C face the same way as
before — a full turn. D has turned sideways — a quarter turn.

Why it happens: A turn is measured by comparing where you face at the end with
where you faced at the start. If you end up facing the opposite way, you have turned
half of a full circle — a half turn. If you end up facing the same way again, you have
gone all the way round — a full turn.

Page 2 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Sample answer for the class discussion: “A has made a half turn, because he was
facing us and now his back is towards us. B and C have made a full turn, because
they are facing us just as before — they went right round. D has made a quarter
turn, because she is now standing sideways.”

Q2 Give examples of real-life situations where you observe turns.

ANSWER

Turns are everywhere. Here are ten from an ordinary day.

SITUATION WHAT TURNS HOW MUCH IT TURNS

Opening a tap the tap handle about a half turn

Opening the lid of a pickle jar the lid two or three full turns

Opening a door the door on its hinge a quarter turn or more

A ceiling fan the blades full turns, again and again

A clock the minute hand one full turn in an hour

A bicycle the wheels and the pedals full turns

Turning the key of a lock the key about a half turn

A merry-go-round in the mela the whole wheel full turns

Rolling a chapati you turn the chapati a little each time small turns

Turning to face your friend behind you you a half turn

Try This: Stand in the school ground and turn slowly. Stop and ask a friend: “Did I
make a quarter turn, a half turn or a full turn?” Then swap.

In-text Questions — Page 33

Page 3 of 101

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Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

The giant wheel, and things that turn
co m
e m.
m l as
Q1
.co
Reema takes two half turns in the same direction. It is like a ______ turn.
m a g
l a se
a g
ANSWER

m
It is like a full turn.

. co ag
e m
g l as
a
1 half turn + 1 half turn

= 1/2 turn + 1/2 turn

co m
m.
= 2/2 turn

m as e
.co
= 1 full turn
a g l
se m
g l a
a
m a s
m .co agl
l a se
a g

co m
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a

co m
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m ase
.co


a g l Page 4 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

after 1st half

Half turn: Reema now faces the opposite way.

Why it happens: One half turn takes Reema to the opposite side of the circle. The
second half turn takes her over the remaining half. Two halves make one whole —
so she is back exactly where she began, facing the same way as at the start.

Check it yourself: Stand up. Turn to face the back wall (half turn). Turn the same
way again. You are facing the front wall once more — a full turn.

Page 5 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Q2 What happens if she takes 2 quarter turns in the same direction? It is like a ______
turn.

ANSWER

It is like a half turn.

1/4 turn + 1/4 turn

= 2/4 turn

= 1/2 turn (a half turn)

start

end

Page 6 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Two quarter turns, one after the other, add up to a half turn.

Why it happens: A full turn is cut into 4 equal quarters. Taking 2 of those 4 quarters
is taking 2/4 of the circle — and 2/4 is the same as 1/2.

Q3 What happens if she takes 4 quarter turns in the same direction? It is like a ____
turn.

ANSWER

It is like a full turn.

1/4 + 1/4 + 1/4 + 1/4

= 4/4 turn

= 1 full turn

Page 7 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start = end

Four quarter turns take you right round the circle — back to the start.

Why it happens: Four quarters make one whole, just as four quarter-chapatis make
one full chapati. So Reema ends up facing exactly the way she started.

Tip: Remember these three by heart — 2 quarters = 1 half, 4 quarters = 1 full, 2
halves = 1 full.

Page 8 of 101

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Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

co m
m.
Write some of the everyday objects that involve turns. For example, taps, __________,
e
Q4

m l as
.co
__________, __________, __________, and __________.

a g
se m
g l a
a
ANSWER

Any five of these will fill the blanks:

. c om ag
s e m clock hands, and bicycle wheels
taps, door handles, bottle lids, ceiling fans,
a
agl
Many more you can add:

co m
m.
a key in a lock

ase
com and a screw l
the steering wheel of a car or an auto
. a g
em or grinder
a screwdriver

aasmixer
l
ag a potter’s wheel
a spinning top (lattu)
m a s
the pages of a book, as you turn them
m .co agl
l a
a merry-go-round or a giant wheel at the mela se
a g
Try This: Walk around your house for five minutes and write down every single thing

co m
you find that turns. Most children find more than fifteen.
m .
m as e
.co a g l
a s em
agl Q5 What is the maximum possible turn in each of these cases? Check and tick. (Clothes
m
clip, Door with hinge, Tongs, Scissors, File cover)

a se
. com a g l
m
ase
ANSWER

a gl
Open each thing as wide as it will go, and compare that opening with a quarter turn — that is,
with the corner of your notebook.

co m
m .
e
OBJECT LESS THAN A 1/4 TURN 1/4 TURN MORE THAN A 1/4 TURN

m l as
.co ✓ a g
em
Clothes clip

a s
agl Door with hinge ✓
.c
✓
s e m
m a
co agl
Tongs

m .
Scissors ✓
ase
a g l
File cover ✓

co m
m .
m as e
.co


a g l Page 9 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Here is the reason for each one.

1. Clothes clip. Press it hard — the two ends open only a small gap. Far less than the corner of
your notebook.
2. Door with hinge. Push it right back till it touches the wall. That is much wider than a corner
— more than a quarter turn.
3. Tongs (chimta). They open a little, to pick up a roti. Less than a quarter turn.
4. Scissors. Open them fully — the blades make a narrow V. Still less than a quarter turn.
5. File cover. Open it right out so it lies flat on the table. That is a half turn — more than a
quarter turn.

Check it yourself: Hold the corner of your notebook against the opening. If the
opening is narrower than the corner, it is less than a quarter turn. If it is wider, it is
more.

Q6 Do any of the above objects make a half turn? Write their names below—

ANSWER

Yes — the file cover, and a door.

1. File cover: open it out completely and it lies flat. The two halves are now in one straight line.
That is exactly a half turn.
2. Door: a door that swings right back and touches the wall behind it has also made a half turn.

Page 10 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

closed

open flat

A file cover opened flat: the front cover has turned half a circle.

Why it happens: When the two parts lie in one straight line, the moving part has
gone from one side right across to the other side — half of a full circle.

Q7 Do any of the above objects make a full turn? Write their names below—

ANSWER

No. None of these five objects makes a full turn.
Each one is joined at a hinge or a joint, and the hinge stops it before it can go all the way round.

Page 11 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Did you know? A spiral-bound notebook is the one cover that can go all the way
round — you can fold its front cover right behind the back cover. That is a full turn.
Things that really do make full turns are a tap handle, a fan, a wheel and a clock
hand.

Q8 Pragya joined a green and yellow straw with paper clips. She holds the green straw
steady and turns the yellow straw around. Observe different turns of the yellow
straw.

ANSWER

Do this yourself with two straws (or two thin sticks) and a paper clip.

1. Join the two straws at one end with a paper clip. The clip is the corner.
2. Hold the green straw still on the table. Do not move it at all.
3. Turn only the yellow straw, slowly, and stop at different places.
4. Each time you stop, look at the opening between the two straws.

This is what you will see, in order:

TURN OF THE YELLOW WHAT THE OPENING LOOKS NAME OF THE
STRAW LIKE ANGLE

a small turn a narrow opening acute angle

1/4 turn a square corner right angle

between 1/4 and 1/2 a wide opening obtuse angle

1/2 turn the two straws in one straight line straight angle

3/4 turn more than a straight line more than a straight angle

full turn the yellow straw is back on the green one full turn

Page 12 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

green

yellow

The green straw stays fixed. The yellow straw turns — here it has made a quarter turn, a right angle.

Sample answer: “When I turn the yellow straw a little, I get an acute angle. At a
quarter turn I get a right angle. Past that I get an obtuse angle, and at a half turn the
two straws lie in one straight line.”

In-text Questions — Page 34

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Class 5 Maths Chapter 3 Angles as Turns
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Angles arise in situations that involve a turn
co m
e m.
m l as
Q1
.co
I made two quarter turns. I wonder what it is called?
m a g
l a se
a g
ANSWER

m
It is a half turn, and the angle it makes is called a straight angle.

. co ag
e m
g l as
a
1/4 turn + 1/4 turn

= 2/4 turn

co m
m.
= 1/2 turn

m as e
.co
The two arms now lie in one straight line
a g l
s m angle is a straight angle
ethe
gl a
So
a
m a s
m .co agl
l a se
a g

co m
m .
m as e
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a
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ase
agl

co m
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m a s e
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a

co m
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m ase
.co


a g l Page 14 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

end

Two quarter turns make a half turn. The two arms make one straight line — a straight angle.

Why it happens: A quarter turn makes a square corner — a right angle. Do it again
and you have gone half way round the circle. The arm has swung from pointing one
way to pointing exactly the opposite way, so both arms now lie flat in a single
straight line.

Tip: Two right angles make one straight angle. That is worth remembering for the
rest of the chapter.

Page 15 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Let Us Do — Pages 34–36
Paper fan, cardboard house, five-sided shape, gymnasts

LET US DO

Q1 (a) Making a paper fan. Take a rectangular paper, fold every 2 cm as shown in the
picture. Paste ice cream sticks as shown below to create a paper fan. Use your
paper fan to show different acute angles and obtuse angles.

1 2 3

4 Paste 5

Paste

Making the paper fan, step by step — 1 fold the sheet every 2 cm, 2 press the pleats,
3 close it up, 4 paste one ice cream stick on the top fold and one on the bottom fold, 5
open the sticks out and the fan is ready.

ANSWER

Here is how to make the fan, step by step.

1. Take a rectangular sheet of paper, about the size of half a newspaper page.
2. Mark lines across it every 2 cm with a ruler.
3. Fold along the first line one way, along the next line the other way, and keep going. This is
called pleating — folding to and fro like a hand fan.
4. Press all the folds flat, then squeeze the pleats together at one end.
5. Paste one ice cream stick on the front of the folded end and one on the back. Let the glue
dry.

Now use the fan to show angles. Hold the bottom stick still on the table. Open the fan by
moving only the top stick.

Page 16 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

HOW FAR YOU OPEN THE FAN WHAT YOU HAVE SHOWN

just a little an acute angle

a bit more, but not a square corner another acute angle

exactly a square corner (a 1/4 turn) a right angle

wider than a square corner, but not flat an obtuse angle

fully open and flat a straight angle (1/2 turn)

acute

Page 17 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Fan opened a little — an acute angle.

Check it yourself: Hold the corner of your notebook inside the opening of the fan. If
the fan is narrower than the corner, it is an acute angle. If it is wider, it is an obtuse
angle.

Q2 (b) You might have built houses using the hard covers of notebooks or cardboard
pieces. Look at the angles marked in the house. What angles are you able to see
in this house? Write your answers as right, acute or obtuse angle. A: ___ B: ___ C:
___ D: ___ E: ___ F: ___ G: ___ H: ___

ANSWER

Reading the marked corners in the picture:

A: obtuse angle B: right angle

C: acute angle D: acute angle

E: acute angle F: right angle

G: right angle H: acute angle

MARK ANGLE WHAT TO LOOK AT

A Obtuse angle The two roof covers lean apart at the top. The opening is much wider than a square corner.

B Right angle The upright pillar stands on the flat book below it — a square corner.

C Acute angle The two cards of the little tent lean close together, so the opening at the top is narrow.

D Acute angle The slanting card meets the flat base in a narrow, sharp corner.

E Acute angle The slanting card meets the upright pillar in a narrow corner.

F Right angle The upright side of the block meets the floor in a square corner.

G Right angle The upright side of the block meets the flat top in a square corner.

H Acute angle The leaning card meets the flat yellow top in a narrow corner.

How to decide, for any corner in the picture:

1. Put the corner of your notebook on the marked corner of the house.
2. If the two sides of the house fit the notebook corner exactly, it is a right angle.

Page 18 of 101

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Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

3. If the opening is narrower than the notebook corner, it is an acute angle.
co m
4. If the opening is wider, it is an obtuse angle.
em.
m l as
m .co a g
l a se
a g

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g right angle
m a s
m .co agl
l a se
a g

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
se m
g l a A right angle — a square corner, like B, F and G.

a c
m .
m a s e
co agl
Tip: Every place where an upright card stands on a flat card gives a right angle. Every

m .
e
place where two cards lean against each other gives an acute angle at the top. A roof
as
a g l
that opens out wide gives an obtuse angle.

co m
m .
m as e
.co


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Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Q3 (c) Make a 5-sided shape with 2 right angles, 2 obtuse angles, and 1 acute angle in
your notebook.

ANSWER

Here is a five-sided shape that has exactly those angles — it looks like a little hut.

acute

D

E C
obtuse obtuse

A B
right right
A hut shape: right angles at A and B, obtuse angles at C and E, and an acute angle at the top, D.

Draw it like this on squared paper.

1. Draw a base line AB of 6 squares.
2. At A go straight up 4 squares to E. At B go straight up 4 squares to C. Now A and B are
square corners — the 2 right angles.
3. Find the middle of the top (3 squares from each side) and go up about 5 more squares. Call
this point D.

Page 20 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

4. Join E to D, and D to C. Do not join E to C.
5. You now have five sides: AB, BC, CD, DE and EA.

Angle A = right angle

Angle B = right angle

Angle C = obtuse angle (wider than a square corner)

Angle E = obtuse angle

Angle D = acute angle (the sharp point at the top)

Why it happens: The two upright sides give the two square corners at the bottom.
Sloping the roof inwards makes the two upper corners open out wider than a square
corner, so they become obtuse. The two slopes meet in a sharp point at the top,
which is acute.

Check it yourself: Test each of the five corners with the corner of another notebook.
You should find exactly 2 that match it, 2 that are wider, and 1 that is narrower.

Page 21 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Q4 (d) Look at the angle formation between the legs of these gymnasts. Identify
whether the angles are acute, obtuse, right or straight.

1

2

3

4

5

Five gymnasts, drawn as stick figures. Beside each one is the angle its legs make,
with an empty box for your answer.

ANSWER

Reading the five pictures from top to bottom:

Page 22 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

GYMNAST HOW WIDE THE LEGS OPEN ANGLE

1st (top) a narrow V — less than a 1/4 turn acute angle

2nd exactly a square corner — a 1/4 turn right angle

3rd wider than a square corner obtuse angle

4th wider still, almost flat obtuse angle

5th (bottom) both legs in one straight line — a 1/2 turn straight angle

obtuse

Page 23 of 101

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Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

The third gymnast: the legs open wider than a square corner — an obtuse angle.
co m
se m.
o m l a
g are the two
m .c The gymnast’s hips are the corner and her twoalegs
seof the angle. As she opens her legs wider, the angle grows: acute first, then
Why it happens:

l a
g at a quarter turn, then obtuse, and at last straight when the legs are in one line
arms
aright
m
(that is called doing the splits).
. co ag
em
g l as
a
Tip: The order never changes — acute, right, obtuse, straight. Each one is bigger
than the one before.

co m
em.
com g l as
m .
In-text Questions — Page 35 a
e
astwo turns
a g l
Adding

a s
com another acute turn? agl
Make an acute turn with the straws or fan. Continue to make another acute turn.
Can the two acute turns together.make
Q1

a s em
ANSWER
agl
Sometimes yes, and sometimes no. It depends on how big the two acute turns are.
co m
m .
se
Try three cases with your straws.

o m l a
gtogether are still narrower
m .c small acute turns. Turn a little, then a little more. The two
1. Two
a
a se than a square corner. Still acute.
agl 2. Two half-of-a-quarter turns. 1/8 turn + 1/8 turn = 2/8 turn = 1/4 turn. That is exactly a
square corner. A right angle, not acute.
se m
com g l a
.
3. Two big acute turns. Turn nearly a quarter, then nearly a quarter again. Together they are
m a
ase
wider than a square corner. Obtuse.

agl
1/8 + 1/8 = 2/8 = 1/4 turn → right angle

co m
m .
e
1/12 + 1/12 = 2/12 = 1/6 turn → still acute
m l as
m .co
1/6 + 1/6 = 2/6 = 1/3 turn → obtuse
a g
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ag
.c
s e m
m a
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g l as
a

com
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m ase
.co


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Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

end

1/12 turn and another 1/12 turn together make a 1/6 turn — still acute.

Why it happens: An angle is acute only while it stays less than a quarter turn. Two
acute turns can add up to less than a quarter turn, exactly a quarter turn, or more
than a quarter turn — so all three answers are possible. The rule is about the total,
not about the two pieces.

Sample answer: “Yes, two acute turns can make another acute turn, but only if they
add up to less than a quarter turn. If they add up to more, the angle becomes
obtuse.”

Page 25 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Angle Measuring Tool — Pages 36–37
Making your own tools to measure turns

ANGLE MEASURING TOOL

Q1 (a) Cut out a circle from a tracing paper and fold it to make 8 equal parts. Attach a
straw to the centre and mark the starting point as shown.

Point (A)

The tracing-paper circle folded into 8 equal parts, with a straw fixed at the centre.
The starting point A is where the straw points now.

ANSWER

Follow these steps carefully. The folds must be neat, or the parts will not be equal.

1. Put a bowl or a glass upside down on tracing paper and draw round it. Cut the circle out.
2. Fold the circle exactly in half. Press the fold. You now have 2 equal parts.
3. Fold it in half again. Press. You now have 4 equal parts.
4. Fold it in half once more. Press. Open it out — you have 8 equal parts.
5. Find the point where all the fold lines cross. That is the centre. Push a straw through it, or
tape the straw so that it can spin about that point.
6. Mark one fold line on the edge of the circle and write A there. That is your starting point. Lay
the straw along it to begin.

Page 26 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

A (start)

1/8

The circle folded into 8 equal parts. The straw starts at A and turns to the next fold — a 1/8 turn.

Why it happens: Every fold cuts each part into two equal halves. So the number of
parts doubles each time — 2, then 4, then 8. Each of the 8 parts is one-eighth of the
full turn.

Tip: Always start the straw from the mark A. A turn only means something when you
say where it started from.

Page 27 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Q2 (b) Show a 1/8 turn of the straw.

ANSWER

Move the straw from the mark A to the very next fold line, going round the circle.

1. Lay the straw exactly on the mark A.
2. Turn it, without lifting it, until it lies on the next fold line.
3. You have crossed one of the 8 equal parts. That is a 1/8 turn.

A

1/8 turn

A 1/8 turn: the straw crosses one of the eight equal parts.

Page 28 of 101

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Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

co m
m.
Why it happens: The circle is cut into 8 equal parts, so crossing 1 part is crossing 1

m as e
l
out of 8 — that is, 1/8 of the whole turn.
.co a g
a s em
gl A 1/8 turn is half of a quarter turn, so it is always an acute angle.
aTip:

co m
e m . ag
Q3 (b)
l as
Show a 2/8 turn. Show a 1/4 turn. Show a 3/8 turn.
g
a
m
ANSWER

co
Count fold lines from A each time.
se m.
om l a
TURN .c FOLD LINES TO CROSS
em ag KIND OF ANGLE
s
WHERE THE STRAW STOPS
a
agl2/8 turn 2 one quarter of the way round right angle

m a s
.co agl
1/4 turn 2 the same place as 2/8 right angle

a s empast the quarter mark
gl
3/8 turn 3 obtuse angle

a
2/8 = 1/4 (both mean 2 parts out of 8)
co m
m .
m ase
l
So a 2/8 turn and a 1/4 turn are the same turn

m .co a g
l a se
ag
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m as e
.co


a g l Page 29 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

A

3/8

A 3/8 turn — three of the eight parts. It is past the quarter mark, so the angle is obtuse.

Why it happens: 8 parts make the full turn, so 2 parts are 2/8. Two-eighths and one-
quarter are equivalent fractions — the same amount written in two ways.

Q4 (b) What angle have you made with a 2/8 turn? A 1/8 turn is half of a quarter turn.

ANSWER

A right angle.

Page 30 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

2/8 turn

= 1/4 turn

= a quarter turn

= a right angle

A

2/8 = 1/4

A 2/8 turn is a quarter turn — a right angle, the square corner.

Why it happens: The hint in the book tells us that 1/8 turn is half of a quarter turn.
Two of those halves make one whole quarter turn — and a quarter turn is exactly a
right angle.

Page 31 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Check it yourself: Hold the corner of your notebook in the opening. It should fit
exactly.

Q5 (b) What angle have you made with a 4/8 turn?

ANSWER

A straight angle.

4/8 turn
= 1/2 turn

= a half turn

The straw now points the opposite way to the start

So the angle is a straight angle

Page 32 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

A

4/8 = 1/2

A 4/8 turn is a half turn. The straw and the starting mark make one straight line.

Why it happens: 4 out of 8 equal parts is half of them. Half of a full turn brings the
straw right across to the other side, so it lies in one straight line with the starting
mark.

Q6 (b) Continue turning by 5/8, 6/8, 7/8, and 8/8. Check when you have completed a 3/4
turn and a full turn.

ANSWER

Keep counting fold lines from A.

Page 33 of 101

as e
Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

co m
m.
TURN SAME AS WHAT IT IS

m as e
5/8 turn
.co
— more than a half turn
a g l
se m
g l a
a
6/8 turn 3/4 turn a three-quarter turn

7/8 turn — almost a full turn

. com ag
8/8 turn 1 whole
e m a full turn — back to A
g l as
a
The 3/4 turn is completed at 6/8, because 6/8 = 3/4

co m
m.
The full turn is completed at 8/8, because 8/8 = 1

m as e
.co a g l
se m
g l a
a
A
m a s
m .co agl
l a se
a g

co m
m .
m ase
.co a g l
se m
g l a
a
se m
6/8 = 3/4 com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m as e
.co


a g l Page 34 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

At 6/8 the straw has made a three-quarter turn.

Why it happens: Divide both the top and the bottom of 6/8 by 2 and you get 3/4 —
the same amount. And when all 8 of the 8 parts have been crossed, nothing is left;
the straw is home again.

Q7 (b) Now, cut out 1/8 part and 2/8 parts of the circle and paste them on a thicker
paper or board. Use these as angle measuring tools.

ANSWER

These two cut-out pieces are your measuring tools. Here is how to make and use them.

1. Cut along the fold lines to take out one single part. That is your 1/8 tool.
2. Cut out two parts joined together. That is your 2/8 tool (the same as a 1/4 tool — a right
angle).
3. Paste each on card or thick paper so it does not bend, and write 1/8 and 2/8 on them.
4. To measure any angle, put the pointed tip of the tool exactly on the corner of the angle, with
one edge along one arm.
5. See if the other arm lies along the other edge. If it does, the angle is 1/8 turn (or 2/8 turn).
6. If the angle is bigger, slide the tool along and use it again. Count how many times it fits —
that is the “combination of measures” the book talks about.

Example: an angle in which the 1/8 tool fits exactly 3 times

= 1/8 + 1/8 + 1/8

= 3/8 turn

Tip: Keep both tools in your geometry box. You will need them for every question on
pages 38 and 39.

Q8 Now, cut out a circle from a tracing paper. First, fold the circle in half, and then fold
it again into 3 equal parts. Attach a straw at the centre of the circle. Mark the
starting point and show the turns equal to 1/6, 2/6, and so on until you complete a
full circle.

ANSWER

This second tool cuts the circle into 6 equal parts instead of 8.

Page 35 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

1. Cut out a fresh circle of tracing paper.
2. Fold it exactly in half. You have 2 equal parts.
3. Now fold that half into 3 equal parts, like folding a letter. Press the folds.
4. Open the circle out. The fold lines have cut it into 2 × 3 = 6 equal parts.
5. Fix the straw at the centre and mark a starting point on the edge.
6. Move the straw one fold line at a time: that is 1/6, then 2/6, then 3/6, 4/6, 5/6 and 6/6.

TURN SAME AS KIND OF ANGLE

1/6 turn — acute

2/6 turn 1/3 turn obtuse

3/6 turn 1/2 turn straight angle

4/6 turn 2/3 turn more than a straight angle

5/6 turn — almost a full turn

6/6 turn 1 whole a full turn

Page 36 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

1/6

One part of the six-part circle: a 1/6 turn, an acute angle.

Why it happens: The first fold gives 2 parts. Folding each of those into 3 gives 3
pieces in each half — that is 6 equal pieces in the whole circle.

Q9 Cut out 1/6 part and 2/6 part of the circle. Fold one of the 1/6 parts into half. Can
you guess what turn of the straw will be equal to half of a 1/6 turn? This is the same
as a 1/12 turn.

ANSWER

Half of a 1/6 turn is a 1/12 turn.

Page 37 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Cut the circle into 6 equal parts

Now cut each part into 2

Number of parts = 6 × 2 = 12
So half of 1/6 = 1/12 of the full turn

start
1/12

Half of a 1/6 part is a 1/12 turn — the smallest tool you will make.

Why it happens: When you cut every piece of a whole into two, you get twice as
many pieces, and each new piece is half as big. Six pieces become twelve, so one-
sixth becomes one-twelfth.

Page 38 of 101

as e
Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

co m
m.
Did you know? Grown-ups measure turns in degrees. A full turn is 360 degrees, so a

as e
caom l
1/12 turn is 30 degrees and a quarter turn is 90 degrees. You will learn about
. a g
m
degrees in later class — in this chapter, turns are enough.

l a se
ag

co m
ag
Let Us Think — Page 37
m .
Finding the starting point of a turn
ase
LET US THINK a g l

co m
e m.
In the following circles, the end points of 1/2, 1/4, and 1/8 turns are shown. Draw

as
Q1

m l
.co
arrows to show the starting points.
a g
se m
g l a
a Each circle already shows the red end arrow, and the green dashed circle shows that the turn
ANSWER

m a s
.co agl
was made clockwise. So to find the start, turn backwards — anti-clockwise — by the amount
written above the circle.
se m
g l a
a
Here is the method, in three steps.

1. Read the size of the turn written above the circle: 1/2, 1/4 or 1/8.
2. Change it into clock hours. A full turn is 12 hours, so 1/2 turn = 6 hours, 1/4 turn = 3 hours,
co m
m .
1/8 turn = 1 and a half hours.
m ase
.co a g l
3. From the red arrow, count back that many hours. Draw the arrow there. That is the start.

a s em
agl CIRCLE TURN RED ARROW (END) COUNT START ARROW

m
POINTS AT BACK POINTS AT

a se
com g l
m. a
1 (blue, top) 1/2 4:30 6 hours 10:30

ase
turn

2 (blue, lower) 1/2 agl
1:30 6 hours 7:30

com
turn

m .
3 (orange, top)
m
1/8 3 o’clock 1½ hours
as e 1:30

.co
turn
a g l
a s em 4 (orange,
gl
1/8 4:30 1½ hours 3 o’clock
a c
.
lower) turn

s e m
m a
.co agl
5 (purple, top) 1/4 10:30 3 hours 7:30

em
turn

a s
6 (purple, 1/4
a gl6 o’clock 3 hours 3 o’clock
lower) turn

co m
m .
m as e
.co


a g l Page 39 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

end

Circle 1 — a 1/2 turn. Blue is the starting arrow you must draw; red is the end arrow already printed.

Page 40 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

end

start

Circle 2 — a 1/2 turn. Blue is the starting arrow you must draw; red is the end arrow already printed.

Page 41 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

end

Circle 3 — a 1/8 turn. Blue is the starting arrow you must draw; red is the end arrow already printed.

Page 42 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

end

Circle 4 — a 1/8 turn. Blue is the starting arrow you must draw; red is the end arrow already printed.

Page 43 of 101

as e
Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m .co a g
l a se
a g
end
co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g

co m
start m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl
Circle 5 — a 1/4 turn. Blue is the starting arrow you must draw; red is the end arrow already printed.

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 44 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

end

Circle 6 — a 1/4 turn. Blue is the starting arrow you must draw; red is the end arrow already printed.

Why it happens: A turn joins a start to an end. If you know the end and the size of
the turn, you can go the other way round to get back to the start — exactly like
walking back the same number of steps you came forward.

Check it yourself: Put your pencil on the start arrow and sweep it clockwise by the
given turn. It must land on the red arrow. If it does not, count again.

Let Us Do — Pages 38–40

Page 45 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Measuring angles and turns with your own tools

LET US DO

Q1 Guess the measures of each of the angles shown below. Then, check using your
angle measuring tools. You may need to use a combination of measures. Also, state
whether each of the angles is acute, right, or obtuse.

The seven angles printed on page 38, each with an empty box beside it for your answer.

ANSWER

There are seven angles with a box beside them. Reading them in order — the three on the left,
then the two in the middle, then the two on the right:

Page 46 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

ANGLE MEASURE OF THE ACUTE / RIGHT / WHAT YOU SEE
TURN OBTUSE

1 1/12 turn acute The two arms open only a little — much less than
a square corner.

2 1/8 turn acute One arm goes straight up, the other leans away by
half a right angle.

3 1/6 turn acute Wider than the first two, but still narrower than a
square corner.

4 1/6 turn acute A narrow V, about the same size as the one before
it.

5 1/4 turn right angle The two arms make an exact square corner.

6 2/6 turn obtuse Wider than a square corner — it opens out well
past the corner of a notebook.

7 3/8 turn obtuse One arm lies flat, the other leans back — much
wider than a square corner.

How to check with your tools

1. Place the tip of the tool exactly on the corner of the angle.
2. Lay one straight edge of the tool along one arm.
3. See where the other edge falls. If it lands on the second arm, you have the measure.
4. If the angle is bigger than the tool, mark where the tool ends, slide it along, and use it again.
Add up what you used.

Angle 6 : 1/6 tool fits twice → 1/6 + 1/6 = 2/6 turn (obtuse)

Angle 7 : 2/8 tool once, then the 1/8 tool once → 2/8 + 1/8 = 3/8 turn (obtuse)

Page 47 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

1/12 turn

Angle 1 — a 1/12 turn.

Page 48 of 101

as e
Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m .co a g
l a se
a g

. com ag
1/8
a s em turn
agl

co m
e m.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g

co m
m .
m as e
.co a g l
se m
g l a Angle 2 — a 1/8 turn.
a
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 49 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

1/6 turn

Angle 3 — a 1/6 turn.

Page 50 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

1/6 turn

Angle 4 — a 1/6 turn.

Page 51 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

1/4 turn

Angle 5 — a 1/4 turn.

Page 52 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

2/6 turn

Angle 6 — a 2/6 turn.

Page 53 of 101

as e
Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m .co a g
l a se
a g

com
e m . ag
g l as
a

co m
e m.
m l as
m .co a g
l a se
a g
m a s
m .co 3/8 turn agl
l a se
a g

co m
m .
m as e
.co a g l
se m
g l a Angle 7 — a 3/8 turn.
a
se m
com g l a
.
Why it happens: Any angle up to a quarter turn is acute, exactly a quarter turn is a
m a
ase
right angle, and anything between a quarter turn and a half turn is obtuse. So once

agl
you know the turn as a fraction, you also know the name.

co m
Tip: Compare with 1/4 every time. 1/12, 1/8 and 1/6 are all smaller than 1/4, so those
m .
m as e
l
angles are acute. 2/6 and 3/8 are bigger than 1/4, so those are obtuse.

m .co a g
l a se
ag
.c
s e m
m a
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 54 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

Q2 Guess the measure of the turns made by the arrow in each of the following cases.
Verify with a combination of angle measuring tools. (a) 1/4 + 1/8 turn or 3/8 turn (b)
___ turn (c) ___ turn (d) ___ turn

ANSWER

In every picture the arrow starts at the top and turns clockwise. Count how many quarters and
eighths it has crossed.

PART WHERE THE ARROW STOPS TURN MADE WRITTEN ANOTHER WAY

(a) in the lower-right quarter 3/8 turn 1/4 + 1/8 (given in the book)

(b) in the lower-left quarter 5/8 turn 1/2 + 1/8

(c) in the upper-right quarter 1/8 turn half of a 1/4 turn

(d) just past the bottom about 5/12 turn 1/4 + 1/6

Page 55 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

end

(b) The arrow starts at the top and stops in the lower-left quarter: a 5/8 turn.

Page 56 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

end

(c) A small clockwise turn into the upper-right quarter: a 1/8 turn.

Page 57 of 101

Class 5 Maths Chapter 3 Angles as Turns AglaSem · NCERT Solutions

start

end

(d) The arrow starts in the upper-right and swings past the bottom: about a 5/12 turn.

(b) 1/2 + 1/8 = 4/8 + 1/8 = 5/8 turn

(d) 1/4 + 1/6 = 3/12 + 2/12 = 5/12 turn

Why it happens: Each picture is divided into four coloured quarters. Count the full
quarters the arrow has passed, then look at how far it has gone into the next quarter
— half of a quarter is 1/8, two-thirds of a quarter is 1/6.

Page 58 of 101

as e
Class 5 Maths Chapter 3 Angles as Turns
a g l AglaSem · NCERT Solutions

co m
m.
Check it yourself: Lay your 2/8 tool and then your 1/8 tool into part (a). Together

m as e
l
they should exactly fill the turn — that is what 1/4 + 1/8 = 3/8 means.

m .co a g
l a se
a g
Q3 (a) Measure each angle in the given shapes. Write the measure of the angles in

co m
ag
terms of turns and describe whether they are acute, obtuse or right angles. —

m .
e
Shape (a)

g l as
a
B' m
co
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g
B
com
m C lasem.
. co ag
e m
g l as
a
se m
com g l a
m . a
ase
A agl
A'
m
m .co
a se
.com a g l
Shape (a) from page 38. The two shaded angles are the ones to measure.
m
ase
agl c
m .
ANSWER
m a s e
m . co
Two shaded angles are marked in this shape — one at A and one at B′.
e agl
g l as
a

co m
m .
m ase
.co


a g l Page 59 of 101