NCERT Solutions for Class 5th Maths Chapter 3 Measuring angles and turns with your own tools — Let Us Do
Book page 38–40 Updated on2026-09-19
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:
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.
How to check with your tools
Place the tip of the tool exactly on the corner of the angle.
Lay one straight edge of the tool along one arm.
See where the other edge falls. If it lands on the second arm, you have the measure.
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 1 — a 1/12 turn.Angle 2 — a 1/8 turn.Angle 3 — a 1/6 turn.Angle 4 — a 1/6 turn.Angle 5 — a 1/4 turn.Angle 6 — a 2/6 turn.Angle 7 — a 3/8 turn.
Why it happens: Any angle up to a quarter turn is acute, exactly a quarter turn is a right angle, and anything between a quarter turn and a half turn is obtuse. So once you know the turn as a fraction, you also know the name.
Tip: Compare with 1/4 every time. 1/12, 1/8 and 1/6 are all smaller than 1/4, so those angles are acute. 2/6 and 3/8 are bigger than 1/4, so those are obtuse.
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
(b) The arrow starts at the top and stops in the lower-left quarter: a 5/8 turn.(c) A small clockwise turn into the upper-right quarter: a 1/8 turn.(d) The arrow starts in the upper-right and swings past the bottom: about a 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.
Check it yourself: Lay your 2/8 tool and then your 1/8 tool into part (a). Together they should exactly fill the turn — that is what 1/4 + 1/8 = 3/8 means.
Q3.
Measure each angle in the given shapes. Write the measure of the angles in terms of turns and describe whether they are acute, obtuse or right angles. — Shape (a)
Shape (a) from page 38. The two shaded angles are the ones to measure.
Answer
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
Two straight lines crossing at C. The shaded angles at A and B′ are each a 1/8 turn.
How to measure them
Put the tip of your 1/8 tool on the point A.
Lay one edge along the arm AB′.
The other edge falls exactly on the arm AB. So ∠A is a 1/8 turn.
Do the same at B′. The 1/8 tool fits there too.
Did you notice? At the crossing point C the two lines make a right angle — a 1/4 turn. That is because 1/8 + 1/8 = 2/8 = 1/4, and the three angles of the triangle A B′ C together make a half turn.
Why it happens: A 1/8 turn is half of a quarter turn, so it is smaller than a square corner. Any angle smaller than a square corner is acute.
Q3.
Measure each angle in the given shapes. — Shape (b)
Shape (b) from page 38. Three angles are shaded.
Answer
This shape is a rhombus — all four sides are the same length. Three angles are shaded: at E, at D and at D′.
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
The rhombus D E D′ E′. The two sharp corners are 1/6 turns; the two wide corners are 2/6 turns.
Check: 1/6 + 2/6 + 1/6 + 2/6 = 6/6 = 1 full turn
Why it happens: Walk right round the edge of the rhombus and you come back facing the way you started — so the four corner turns together make one full turn. That is a good way to check your four answers.
Tip: In a rhombus the opposite corners are always equal. That is why D and D′ match, and E and E′ match.
Q3.
Measure each angle in the given shapes. — Shape (c)
Shape (c) from page 38. Two angles are shaded and one carries a square corner mark.
Answer
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
The shape F G F′ G′. The little square at F′ is the book’s mark for a right angle.
Why it happens: The small square drawn in a corner is the usual sign for a right angle, so ∠F′ is a 1/4 turn without any measuring. F is a sharp point, so it is acute; G opens out much wider than a square corner, so it is obtuse.
Check it yourself: Your 1/8 tool should fit exactly at F. Your 1/6 tool should fit twice at G.
Q4.
Draw angles for the given measures of turns using the given lines. (1/2 turn, 1/4 turn, 1/4 turn, 1/12 turn, 1/8 turn)
Answer
Method for every one of the five lines:
Pick one end of the given line. That end is the corner of your angle.
Put your measuring tool with its tip on that corner and one edge along the line.
Make a small mark where the other edge of the tool falls.
Draw a new line from the corner through that mark. The two lines now make the required turn.
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
1/2 turn on the upright line: the new arm points the opposite way, making one straight line.1/4 turn on the slanting line: a square corner.1/4 turn on the flat line: a square corner.1/12 turn: a very narrow opening.1/8 turn on the upright line: half of a square corner.
Tip: You may turn either way — clockwise or anti-clockwise. Both give an angle of the right size.
Q5.
Draw the angles formed by the following turns in your notebook. 1/2 turn, 1/4 turn, 2/4 turn, 1/6 turn, 4/6 turn, 3/12 turn, 1/2 + 1/4 turn, and 1/8 + 1/6 turn.
Answer
First work out what each turn is, then draw it. Two pairs in this list are secretly the same turn.
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
7/24
obtuse angle — a little more than a quarter turn
The two additions, step by step
1/2 + 1/4 Step 1: make the bottoms the same → 1/2 = 2/4 Step 2: add → 2/4 + 1/4 = 3/4 turn
1/8 + 1/6 Step 1: 8 and 6 both go into 24 Step 2: 1/8 = 3/24 and 1/6 = 4/24 Step 3: add → 3/24 + 4/24 = 7/24 turn Step 4: compare with a quarter → 1/4 = 6/24, and 7/24 is a little more, so the angle is obtuse
A 4/6 turn — two-thirds of the way round the circle, well past a straight angle.A 1/2 + 1/4 = 3/4 turn.A 1/8 + 1/6 = 7/24 turn — just past a square corner, so it is obtuse.
Tip: 2/4 is the same as 1/2, and 3/12 is the same as 1/4. Equivalent fractions give equal turns.
Q6.
When the minute hand moves by 15 minutes, it has made a _______ turn of the circle.
Answer
A 1/4 turn (a quarter turn).
A full turn of the minute hand takes 60 minutes 15 minutes out of 60 = 15/60 15/60 = 1/4 turn
The hand starts at 3 and moves 15 minutes clockwise — it stops at 6. That is a quarter turn.
Why it happens: Divide the top and the bottom of 15/60 by 15 and you get 1/4. So a quarter of an hour is a quarter turn of the minute hand.
Drawing the final position: the hand in the book starts at 3. Move it three numbers on — to 6 — and draw it there.
Q6.
When the minute hand moves by 30 minutes, it has made a _______ turn of the circle.
Answer
A 1/2 turn (a half turn).
30 minutes out of 60 = 30/60 30/60 = 1/2 turn
The hand starts at 6 and moves 30 minutes clockwise — it stops at 12. That is a half turn.
Why it happens: Half an hour is half of 60 minutes, so the hand goes half way round the clock face. It ends up pointing exactly the opposite way — a straight angle.
Q6.
When the minute hand moves by 45 minutes, it has made a _______ turn of the circle.
Answer
A 3/4 turn (a three-quarter turn).
45 minutes out of 60 = 45/60 Divide both by 15 → 3/4 turn
The hand starts at 9 and moves 45 minutes clockwise — 9 to 12, 12 to 3, 3 to 6. It stops at 6.
Why it happens: 45 minutes is three lots of 15 minutes, and each 15 minutes is a quarter turn. Three quarters make a 3/4 turn.
Check it yourself: Count the numbers on the clock: 9 → 10 → 11 → 12 → 1 → 2 → 3 → 4 → 5 → 6. That is 9 numbers, and each number is 5 minutes. 9 × 5 = 45 minutes.
Q6.
When the minute hand has turned by 1/12 of a full turn, it has moved by ______ minutes.
Answer
5 minutes.
A full turn = 60 minutes 1/12 of a full turn = 60 ÷ 12 = 5 minutes
The hand starts at 1 and turns 1/12 of the circle — it moves on to 2, which is 5 minutes later.
Why it happens: The clock face is already cut into 12 equal parts by the numbers 1 to 12. Moving from one number to the next is exactly 1/12 of the circle, and that takes 5 minutes.
Tip: One number to the next = 5 minutes. This is worth learning by heart.
Q6.
When the minute hand has turned a full-circle, it has moved by ______ minutes.
The hand starts at 12 and comes back to 12. One full turn = 60 minutes.
Why it happens: The minute hand comes back to where it began only when the whole hour is over. That is what an hour means on a clock face.
Q6.
When the minute hand has turned by 1/6 of a full turn, it has moved by _____ minutes.
Answer
10 minutes.
A full turn = 60 minutes 1/6 of a full turn = 60 ÷ 6 = 10 minutes
The hand starts at 2 and turns 1/6 of the circle — it stops at 4, ten minutes later.
Why it happens: A sixth of the clock face is two of the twelve gaps between the numbers. Each gap is 5 minutes, so two gaps are 10 minutes.
Check it yourself: 1/6 = 2/12, and 2 gaps × 5 minutes = 10 minutes. The two ways agree.
Q6.
When the minute hand has turned by 4/12 of a full turn, it has moved by _____ minutes.
Answer
20 minutes.
Step 1: simplify the fraction → 4/12 = 1/3 Step 2: a full turn = 60 minutes Step 3: 1/3 of 60 = 60 ÷ 3 = 20 minutes
The hand starts at 4 and turns 4/12 of the circle — it stops at 8, twenty minutes later.
Why it happens: 4/12 means 4 of the 12 gaps between the clock numbers. Each gap is 5 minutes, so 4 × 5 = 20 minutes. Simplifying the fraction gives the same answer, which is a good check.
Note: In the Hindi edition of the book this part reads “1/4 of a full turn”, and then the answer is 15 minutes. Answer whichever fraction is printed in your own copy.