NCERT Solutions for Class 5 Maths Chapter 3 Angles As Turns – step-by-step answers to every exercise and in-text question of the chapter, as per the latest NCERT syllabus for 2027. Read them online or download the free question-answer PDF.
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.
NCERT Solutions for Class 5 Maths Chapter 3 Angles As Turns PDF
All the answers are on this page below. The PDF also explains every answer – why it is right and how to check it – so download it for revision.
| Chapter | Download | |
|---|---|---|
| Solutions PDF (English medium) | Angles As Turns | View PDF |
| Solutions PDF (Hindi medium) | घुमाव के रूप में कोण | View PDF |
NCERT Solutions for Class 5 Maths Chapter 3 Angles As Turns – Questions and Answers
All 46 questions of the chapter (textbook pages 32 – 41) are answered below, in the order of the book – in-text questions, activities and the end-of-chapter exercises. Each answer is written the way you would write it in the exam.
In-text Questions — Page 32Let us play “Statue”
B and C have made a full turn. A has made a half turn. (D has made a quarter turn.)
How we know: A was facing us and now his back is towards us — he faces the opposite way, so it is a half turn. B and C face us again, just as at the start, so they went all the way round — a full turn.
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 |
In-text Questions — Page 33The giant wheel, and things that turn
It is like a full turn.
= 1/2 turn + 1/2 turn
= 2/2 turn
= 1 full turn
It is like a half turn.
= 2/4 turn
= 1/2 turn (a half turn)
It is like a full turn.
= 4/4 turn
= 1 full turn
Any five of these will fill the blanks:
| Object | Less than a 1/4 turn | 1/4 turn | More than a 1/4 turn |
|---|---|---|---|
| Clothes clip | |||
| Door with hinge | |||
| Tongs | |||
| Scissors | |||
| File cover |
Compare the widest opening of each object with a square corner (a 1/4 turn):
| Object | Less than a 1/4 turn | 1/4 turn | More than a 1/4 turn |
|---|---|---|---|
| Clothes clip | ✓ | ||
| Door with hinge | ✓ | ||
| Tongs | ✓ | ||
| Scissors | ✓ | ||
| File cover | ✓ |
Yes — the file cover, and a door.
- 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.
- Door: a door that swings right back and touches the wall behind it has also made a half turn.
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.
| Turn of the yellow straw | What the opening looks like | Name of the 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 |
In-text Questions — Page 34Angles arise in situations that involve a turn
It is a half turn, and the angle it makes is called a straight angle.
= 2/4 turn
= 1/2 turn
The two arms now lie in one straight line
So the angle is a straight angle
Let Us Do — Pages 34–36Paper fan, cardboard house, five-sided shape, gymnasts
Make the fan: fold the paper to and fro every 2 cm, press the pleats together at one end and paste an ice cream stick on each outer fold.
Now use the fan to show angles. Hold the bottom stick still on the table. Open the fan by moving only the top stick.
| 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) |
A: ______ B: ______
C: ______ D: ______
E: ______ F: ______
G: ______ H: ______
Reading the marked corners in the picture:
C: acute angle D: acute angle
E: acute angle F: right angle
G: right angle H: obtuse angle
Sample answer — a hut shape:
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)
Reading the five pictures from top to bottom:
| 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 |
In-text Questions — Page 35Adding two turns
Sometimes yes, and sometimes no. It depends on how big the two acute turns are.
1/12 + 1/12 = 2/12 = 1/6 turn → still acute
1/6 + 1/6 = 2/6 = 1/3 turn → obtuse
Angle Measuring Tool — Pages 36–37Making your own tools to measure turns
Steps: Cut a circle out of tracing paper. Fold it in half three times, then open it — the fold lines divide it into 8 equal parts. Fix a straw at the centre (where the folds meet) and mark one fold line on the edge as the starting point A.
Move the straw from the mark A to the very next fold line, going round the circle.
Count fold lines from A each time.
| Turn | Fold lines to cross | Where the straw stops | Kind of angle |
|---|---|---|---|
| 2/8 turn | 2 | one quarter of the way round | right angle |
| 1/4 turn | 2 | the same place as 2/8 | right angle |
| 3/8 turn | 3 | past the quarter mark | obtuse angle |
So a 2/8 turn and a 1/4 turn are the same turn
A right angle.
= 1/4 turn
= a quarter turn
= a right angle
A straight angle.
= 1/2 turn
= a half turn
The straw now points the opposite way to the start
So the angle is a straight angle
Keep counting fold lines from A.
| Turn | Same as | What it is |
|---|---|---|
| 5/8 turn | — | more than a half turn |
| 6/8 turn | 3/4 turn | a three-quarter turn |
| 7/8 turn | — | almost a full turn |
| 8/8 turn | 1 whole | a full turn — back to A |
The full turn is completed at 8/8, because 8/8 = 1
I cut out one part — my 1/8 tool — and two joined parts — my 2/8 tool (the same as a 1/4 turn, a right angle) — and pasted them on card. To measure an angle, I put the tip of a tool on the corner with one edge along one arm. If the angle is bigger, I use the tools again and add the turns.
Folding the circle in half and then into 3 gives 2 × 3 = 6 equal parts. Turning the straw one fold at a time from the starting point gives:
| 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 |
Half of a 1/6 turn is a 1/12 turn.
Now cut each part into 2
Number of parts = 6 × 2 = 12
So half of 1/6 = 1/12 of the full turn
Let Us Think — Page 37Finding the starting point of a turn
The green arrows show that each turn was made clockwise, so from each red end arrow go back anti-clockwise by the turn. Draw the start arrow here:
| Circle | Turn | Red arrow (end) points at | Count back | Start arrow points at |
|---|---|---|---|---|
| 1 (blue, top) | 1/2 turn | 4:30 | 6 hours | 10:30 |
| 2 (blue, lower) | 1/2 turn | 1:30 | 6 hours | 7:30 |
| 3 (orange, top) | 1/8 turn | 3 o’clock | 1½ hours | 1:30 |
| 4 (orange, lower) | 1/8 turn | 4:30 | 1½ hours | 3 o’clock |
| 5 (purple, top) | 1/4 turn | 10:30 | 3 hours | 7:30 |
| 6 (purple, lower) | 1/4 turn | 6 o’clock | 3 hours | 3 o’clock |
Let Us Do — Pages 38–40Measuring angles and turns with your own tools
Angles numbered as in the figure:
| Angle | Measure of the turn | Acute / right / obtuse | What you see |
|---|---|---|---|
| 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. |
Every arrow turns clockwise. In (a), (b) and (c) it starts pointing straight up; in (d) it starts pointing to the upper right.
| 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 |
(d) 1/4 + 1/6 = 3/12 + 2/12 = 5/12 turn
Two shaded angles are marked in this shape — one at A and one at B′.
| Angle | Measure as a turn | Name |
|---|---|---|
| ∠A (between AB′ and AB) | 1/8 turn | acute angle |
| ∠B′ (between B′A and B′A′) | 1/8 turn | acute angle |
Three angles are shaded — at E, D and D′. (The fourth corner, E′, is not shaded.)
| Angle | Measure as a turn | Name |
|---|---|---|
| ∠E (top) | 2/6 turn (same as 1/3 turn) | obtuse angle |
| ∠D (left) | 1/6 turn | acute angle |
| ∠D′ (right) | 1/6 turn | acute angle |
| ∠E′ (bottom, not shaded) | 2/6 turn | obtuse angle |
Three angles are marked in this four-sided shape: at F, at G, and the small square mark at F′.
| Angle | Measure as a turn | Name |
|---|---|---|
| ∠F (bottom-left) | 1/8 turn | acute angle |
| ∠G (bottom-right) | 2/6 turn | obtuse angle |
| ∠F′ (top-right, square mark) | 1/4 turn | right angle |
| ∠G′ (top-left, not marked) | a little more than 1/4 turn | obtuse angle |
At one end of each given line, put the tip of the right tool with one edge along the line, and draw the new arm along the other edge.
| Given line | Turn asked for | Tool to use | What your drawing will look like |
|---|---|---|---|
| the tall line, top-left | 1/2 turn | two 1/4 tools | the new line carries straight on — a straight angle |
| the slanting line, top-middle | 1/4 turn | the 2/8 tool | a square corner |
| the flat line, bottom-left | 1/4 turn | the 2/8 tool | a square corner |
| the slanting line, bottom-middle | 1/12 turn | the 1/12 tool | a very narrow acute angle |
| the tall line, right | 1/8 turn | the 1/8 tool | an acute angle, half a square corner |
Work out each turn, then draw it with your angle tools.
| Turn asked for | Simplest form | What the angle is |
|---|---|---|
| 1/2 turn | 1/2 | straight angle — one straight line |
| 1/4 turn | 1/4 | right angle — a square corner |
| 2/4 turn | 1/2 | straight angle — the same as the first one |
| 1/6 turn | 1/6 | acute angle |
| 4/6 turn | 2/3 | more than a straight angle (past halfway round) |
| 3/12 turn | 1/4 | right angle — the same as the second one |
| 1/2 + 1/4 turn | 3/4 | three-quarter turn — more than a straight angle |
| 1/8 + 1/6 turn | a little more than 1/4 | obtuse angle |
Step 1: make the bottoms the same → 1/2 = 2/4
Step 2: add → 2/4 + 1/4 = 3/4 turn
so 1/8 + 1/6 is more than 1/8 + 1/8 = 1/4 turn
→ a little more than a right angle = obtuse angle
A 1/4 turn (a quarter turn).
15 minutes out of 60 = 15/60
15/60 = 1/4 turn
A 1/2 turn (a half turn).
30/60 = 1/2 turn
A 3/4 turn (a three-quarter turn).
Divide both by 15 → 3/4 turn
5 minutes.
1/12 of a full turn = 60 ÷ 12
= 5 minutes
60 minutes — that is, one whole hour.
= 60 minutes
= 1 hour
10 minutes.
1/6 of a full turn = 60 ÷ 6
= 10 minutes
20 minutes.
Step 2: a full turn = 60 minutes
Step 3: 1/3 of 60 = 60 ÷ 3 = 20 minutes
Which direction? — Page 40Clockwise and anti-clockwise
The hands of a clock move from 12 to 1, 2, 3 and so on. This direction is called clockwise. The opposite direction — 12 to 11, 10, 9 — is called anti-clockwise.
Look at which way the creature’s head was pointing before, and which way it points after.
| Creature | Head at first | Head after the turn | Direction |
|---|---|---|---|
| Ladybird | pointing left | pointing up | Clockwise |
| Snail | pointing down | pointing left | Clockwise |
| Bee | pointing left | pointing down | Anti-clockwise |
| Ant | pointing up | pointing left | Anti-clockwise |
To open them you turn anti-clockwise. To close them you turn clockwise.
| What you do | Direction |
|---|---|
| Opening a tap | anti-clockwise |
| Closing a tap | clockwise |
| Unscrewing the lid of a jar | anti-clockwise |
| Screwing the lid back on | clockwise |
| Loosening a nut with a spanner | anti-clockwise |
| Tightening a nut | clockwise |
Fun with Turns — Pages 40–41Turning to face a direction
| Starting Direction | Turns | Ending Direction |
|---|---|---|
| North | Two right angles, clockwise | |
| South | Two right angles, anti-clockwise | |
| East | Four right angles, anti-clockwise | |
| West | Four right angles, clockwise | |
| North | 5 right angles, clockwise | |
| South | 3 right angles clockwise, 1/2 right angle clockwise, 1/2 right angle clockwise | |
| West | right angles clockwise, four 1/2 right angles anti-clockwise |
Each right angle turns you to the next direction on the compass; 4 right angles bring you back to where you started.
| Starting Direction | Turns | Ending Direction |
|---|---|---|
| North | Two right angles, clockwise | South |
| South | Two right angles, anti-clockwise | North |
| East | Four right angles, anti-clockwise | East |
| West | Four right angles, clockwise | West |
| North | 5 right angles, clockwise | East |
| South | 3 right angles clockwise, 1/2 right angle clockwise, 1/2 right angle clockwise | South |
| West | (number missing in the book) right angles clockwise, four 1/2 right angles anti-clockwise | West (if the missing number is 2) |
She will face the ice cream cart.
The toy shop is straight in front of Padma and the ice cream cart is straight behind her. A half turn makes her face the opposite way, so the cart comes in front of her.
She can take a half turn anti-clockwise instead. She will face the ice cream cart just the same.
Other ways that also work:
- two quarter turns clockwise (one after the other)
- two quarter turns anti-clockwise
- two right angles, either way round
- one and a half turns clockwise — the extra full turn changes nothing
Chapter 3 of 15 – Maths
- Previous: Chapter 2 Fractions
- Next: Chapter 4 We the Travellers Ii
- All chapters: NCERT Solutions Class 5 Maths
Also for This Chapter
NCERT Solutions Class 5 Maths Chapter 3 Angles As Turns – Overview
| Class | Class 5 |
| Subject | Maths |
| Chapter | 3 – Angles As Turns |
| Textbook pages | 32 – 41 |
| Questions solved | 46 |
| Session | 2027 |
| Format | Full answers on this page + PDF |
NCERT Solutions Class 5 Maths Chapter 3 – FAQs
Where can I download NCERT Solutions Class 5 Maths Chapter 3 Angles As Turns PDF?
Read every answer on this page, or download the free PDF from the table at the top.
Is this for the 2027 session?
Yes, it follows the latest NCERT Class 5 Maths book for 2027.
How many questions are solved in NCERT Class 5 Maths Chapter 3?
All 46 questions of the chapter (textbook pages 32 – 41) – the in-text questions, activities and the end-of-chapter exercises.
How should I use these solutions?
Read the chapter in the NCERT book first, attempt the questions yourself, then check your answers here.