NCERT Solutions Ganita Prakash Chapter 2 – 31Section 2.8 Special Types of Angles — In-text Questions
Book page 28 Updated on2026-09-05
Q1.
Let us consider a straight angle ∠AOB. Observe that any ray OC divides it into two angles, ∠AOC and ∠COB. Is it possible to draw OC such that the two angles are equal to each other in size? Justify why the two angles are equal.
Answer
Yes, it is possible — and paper folding shows it beautifully.
Take a rectangular sheet, mark the straight angle ∠AOB along one edge, and fold the paper so that ray OB falls exactly on ray OA. The crease that passes through O is the required ray OC.
The ray OC divides the straight angle ∠AOB into two equal right angles of 90° each.
Justification: when the paper is folded, ∠COB comes to lie exactly on top of ∠AOC — vertex on vertex and arm on arm. By superimposition the two angles are therefore equal.
∠AOC + ∠COB = 180° and ∠AOC = ∠COB so each angle = 180° ÷ 2 = 90°
What we have just made: each of these two equal angles is a right angle. So a straight angle contains exactly two right angles, and OC is perpendicular to AB.
Q2.
If a straight angle is formed by half of a full turn, how much of a full turn will form a right angle?
Answer
A quarter of a full turn.
1 straight angle = ½ of a full turn 1 straight angle = 2 right angles 1 right angle = ½ × ½ = ¼ of a full turn
In degrees:
Full turn = 360° → straight angle = 180° → right angle = 90°
Tip: a right angle looks like the letter L, and two lines meeting at a right angle are called perpendicular lines. But be careful — a shape that merely looks like an L is a right angle only if it is exactly half of a straight angle.
Q3.
Angles are classified in three groups as shown. Right angles are shown in the second group. What could be the common feature of the other two groups?
Answer
The groups are decided by comparing each angle with a right angle.
Group
Common feature
Name
First
every angle is smaller than a right angle — less than a quarter turn
Acute angles
Second
every angle is exactly a quarter turn
Right angles
Third
every angle is greater than a right angle but smaller than a straight angle — between a quarter turn and a half turn
Obtuse angles
The five kinds of angles — acute, right, obtuse, straight and reflex.
Why the right angle is the yardstick: it is easy to make (fold a paper twice) and easy to recognise (the corner of a book). So every other angle is described as "less than", "equal to" or "more than" a right angle.