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NCERT Solutions Ganita Prakash Chapter 2 Figure it Out — Comparing Angles

Book page 23 Updated on2026-09-05

Q1.
Fold a rectangular sheet of paper, then draw a line along the fold created. Name and compare the angles formed between the fold and the sides of the paper. Make different angles by folding a rectangular sheet of paper and compare the angles. Which is the largest and smallest angle you made?
Answer

Fold the sheet so that the crease cuts across two opposite sides. Mark the crease as EF, with E and F on the two sides. Four angles are formed:

∠AEF,   ∠BEF,   ∠DFE,   ∠CFE

On comparing (by tracing and superimposing them):

  • If the crease is slanting, then ∠AEF and ∠CFE are the two obtuse angles, and ∠BEF and ∠DFE are the two acute angles. So ∠AEF = ∠CFE > ∠BEF = ∠DFE.
  • If the crease is folded so that it runs straight across, all four angles become equal right angles.
∠AEF + ∠BEF = 180°   (they make a straight angle along the edge)
Why: the two angles on one side of the paper together make a straight line, so making one of them larger automatically makes the other smaller. The largest angle you can make this way is just below a straight angle (180°), and the smallest is a very thin sliver near 0°.
Q2.
In each case, determine which angle is greater and why. a. ∠AOB or ∠XOY b. ∠AOB or ∠XOB c. ∠XOB or ∠XOC. Discuss with your friends on how you decided which one is greater.
Answer
AXYBC32°O
The rays OA, OX, OY and OB from the vertex O. B and C lie on the same ray, so OB and OC are one arm. Measured: ∠AOB ≈ 90°, ∠XOB ≈ 60°, ∠XOY ≈ 32°.

a. ∠AOB is greater.

∠AOB = ∠AOX + ∠XOY + ∠YOB

The whole is bigger than any of its parts, and ∠XOY is only a part of ∠AOB. Measured with a protractor, ∠AOB ≈ 90° while ∠XOY ≈ 32°.

b. ∠AOB is greater.

∠AOB = ∠AOX + ∠XOB   so   ∠AOB > ∠XOB
(≈ 90° against ≈ 60°)

c. Neither — they are equal: ∠XOB = ∠XOC.

Why (c) surprises many students: B and C lie on the same ray from O. So OB and OC are two names for one and the same arm, and both angles are made by exactly the same pair of arms. Making an arm longer does not make the angle bigger — only turning does.
Q3.
Which angle is greater: ∠XOY or ∠AOB? Give reasons.
Answer
XAYB∠XOY ≈ 111°∠AOB ≈ 55°O
All four rays start at O. Measured on the page, ∠XOY ≈ 111° and ∠AOB ≈ 55° — but neither angle lies inside the other.

∠XOY is the greater angle. Measuring the printed figure with a protractor gives

∠XOY ≈ 111°     ∠AOB ≈ 55°

But you cannot get this answer just by looking, and the trick used in question 2 does not work here either.

Why the “part of the whole” argument fails: in question 2 one angle lay completely inside the other. Here the four rays are interleaved — going anticlockwise from OB the order is B, Y, A, X. So ∠AOB sticks out below OY while ∠XOY sticks out above OA: neither angle contains the other. Nothing can be concluded by inspection alone.

What to do instead:

  1. Superimposition — trace ∠AOB on tracing paper, put the traced vertex on O with OA along OX, and see where OB falls.
  2. Measurement — read both angles with a protractor and compare the numbers. This settles it at once.
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