NCERT Solutions for Class 5th Maths Chapter 3 Making your own tools to measure turns — Angle Measuring Tool
Book page 36–37 Updated on2026-09-19
Q1.
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.
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.
Put a bowl or a glass upside down on tracing paper and draw round it. Cut the circle out.
Fold the circle exactly in half. Press the fold. You now have 2 equal parts.
Fold it in half again. Press. You now have 4 equal parts.
Fold it in half once more. Press. Open it out — you have 8 equal parts.
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.
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.
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.
Q2.
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.
Lay the straw exactly on the mark A.
Turn it, without lifting it, until it lies on the next fold line.
You have crossed one of the 8 equal parts. That is a 1/8 turn.
A 1/8 turn: the straw crosses one of the eight equal parts.
Why it happens: The circle is cut into 8 equal parts, so crossing 1 part is crossing 1 out of 8 — that is, 1/8 of the whole turn.
Tip: A 1/8 turn is half of a quarter turn, so it is always an acute angle.
Q3.
Show a 2/8 turn. Show a 1/4 turn. Show a 3/8 turn.
Answer
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
2/8 = 1/4 (both mean 2 parts out of 8) So a 2/8 turn and a 1/4 turn are the same turn
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.
What angle have you made with a 2/8 turn? A 1/8 turn is half of a quarter turn.
Answer
A right angle.
2/8 turn = 1/4 turn = a quarter turn = a right angle
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.
Check it yourself: Hold the corner of your notebook in the opening. It should fit exactly.
Q5.
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
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.
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.
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 3/4 turn is completed at 6/8, because 6/8 = 3/4 The full turn is completed at 8/8, because 8/8 = 1
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.
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.
Cut along the fold lines to take out one single part. That is your 1/8 tool.
Cut out two parts joined together. That is your 2/8 tool (the same as a 1/4 tool — a right angle).
Paste each on card or thick paper so it does not bend, and write 1/8 and 2/8 on them.
To measure any angle, put the pointed tip of the tool exactly on the corner of the angle, with one edge along one arm.
See if the other arm lies along the other edge. If it does, the angle is 1/8 turn (or 2/8 turn).
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.
Cut out a fresh circle of tracing paper.
Fold it exactly in half. You have 2 equal parts.
Now fold that half into 3 equal parts, like folding a letter. Press the folds.
Open the circle out. The fold lines have cut it into 2 × 3 = 6 equal parts.
Fix the straw at the centre and mark a starting point on the edge.
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
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.
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
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.
Did you know? Grown-ups measure turns in degrees. A full turn is 360 degrees, so a 1/12 turn is 30 degrees and a quarter turn is 90 degrees. You will learn about degrees in a later class — in this chapter, turns are enough.