NCERT Solutions Ganita Prakash Chapter 2 – 40Section 2.9 Make your own Protractor — In-text Questions

Book page 38 Updated on2026-09-05

Q1.

The measure of half a circle is ½ of a full turn. So, the measure of half a turn = ½ of ____ = 180°. The measure of a ¼ turn = ¼ of 360° = ________. When folded, this is ⅛ of the circle, or ⅛ of a turn, or ⅛ of 360°, or ¼ of 180° or ½ of 90° = ________. Continuing with another half fold, we get an angle of measure ________.

Answer

Each fold halves the angle. Fill the blanks like this:

Fold	Part of a full turn	Working	Angle
Whole circle	1	—	360°
1st fold (semicircle)	½	½ of 360°	180°
2nd fold (quarter)	¼	¼ of 360° = ½ of 180°	90°
3rd fold	⅛	⅛ of 360° = ¼ of 180° = ½ of 90°	45°
4th fold	1/16	½ of 45°	22.5°

So the blanks are 360°, 90°, 45° and 22.5°. The new creases also give 180° − 45° = 135°, and later 67.5°, 112.5° and 157.5°.

Tip: write 0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°, 157.5° and 180° along the edge of your paper protractor — it can then measure any of these angles without a scale.

Q2.

Think! In Fig. 2.19, we have ∠AOB = ∠BOC = ∠COD = ∠DOE = ∠EOF = ∠FOG = ∠GOH = ∠HOI = _____. Why?

Answer

Each of these angles is 22.5°.

The straight angle ∠AOI = 180°
It has been folded into 8 equal parts
Each part = 180° ÷ 8 = 22.5°

Why they are all equal: every crease was made by folding the previous angle exactly in half, so at each stage the two new angles fell exactly on each other. Halving 180° three times gives 90°, then 45°, then 22.5° — and the eight small angles produced are copies of one another.

Check it yourself: 22.5° × 8 = 180° ✔ and 22.5° × 16 = 360°, one full turn.

Q3.

Identify the angle bisectors in your handmade protractor. Try to make different angles using the concept of angle bisector through paper folding.

Answer

A line that cuts an angle into two equal parts is called the angle bisector of that angle. In the paper protractor every crease is a bisector of the angle formed by the two creases beside it.

Crease at	Bisects the angle	Into two angles of
90°	the straight angle 0°–180°	90° each
45°	the right angle 0°–90°	45° each
135°	the right angle 90°–180°	45° each
22.5°	the angle 0°–45°	22.5° each
67.5°	the angle 45°–90°	22.5° each

Try This: fold once more to get 11.25°, and combine creases to build angles such as 22.5 + 45 = 67.5°, or 90 + 22.5 = 112.5°. Paper folding alone can make a surprising number of exact angles.

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