NCERT Solutions Ganita Prakash Chapter 2 Figure it Out — Classifying Angles
Book page 31 & 32 Updated on2026-09-05
Q1.
Identify acute, right, obtuse and straight angles in the previous figures.
Answer
Compare every angle with a right angle (use the corner of your notebook as a tester):
The five kinds of angles — acute, right, obtuse, straight and reflex.
Type
How to spot it
Where it appears in the earlier figures
Acute
smaller than the notebook corner
the narrow angles of the rotating arms; Vidya's book in Case 1 and Case 2; the thin angles at a paper fold
Right
fits the notebook corner exactly
the four angles at the crossing creases; corners of the rectangular sheet; Vidya's book opened as an L
Obtuse
bigger than the corner but not a straight line
the wide angles at a slanting crease; Vidya's book in Case 5
Straight
the two arms lie in one straight line
∠AOB when the book is opened flat on the table (Case 6)
Q2.
Make a few acute angles and a few obtuse angles. Draw them in different orientations.
Answer
Draw them opening upwards, downwards, to the left and to the right — the direction in which an angle points does not change its type.
Acute angles (45°, 60°, 80°) and obtuse angles (100°, 135°, 160°) drawn in different orientations.
Acute angles (less than 90°): try 20°, 45°, 60° and 80°.
Obtuse angles (between 90° and 180°): try 100°, 120°, 135° and 160°.
Check it yourself: hold the corner of your notebook at the vertex of each angle you drew. If your angle hides inside the corner it is acute; if it opens out beyond the corner it is obtuse.
Q3.
Do you know what the words acute and obtuse mean? Acute means sharp and obtuse means blunt. Why do you think these words have been chosen?
Answer
Because the words describe exactly how the angles look.
An acute angle has a narrow opening, so the vertex ends in a sharp point — like the tip of a pencil, a needle or a thorn.
An obtuse angle has a wide opening, so the vertex looks flat and blunt — like the edge of a spoon or a rounded stone.
The five kinds of angles — acute, right, obtuse, straight and reflex.
The idea: the smaller the turn between the arms, the sharper the corner appears; the larger the turn, the more the corner opens out and flattens. So "sharp" and "blunt" are good everyday names for "less than 90°" and "more than 90°".
Did you know? Doctors also use these words — an acute illness is sharp and sudden, while a blunt object causes an obtuse injury.
Q4.
Find out the number of acute angles in each of the figures below. What will be the next figure and how many acute angles will it have? Do you notice any pattern in the numbers?
Answer
The three figures of page 32 — 3, 12 and 21 acute angles. Each new inner triangle turns one small triangle into four.
Figure
Small triangles in it
Number of acute angles
1st
1
3
2nd
4
12
3rd
7
21
4th (next)
10
30
The next figure is made by joining the midpoints of one more small triangle, and it contains 30 acute angles.
Why 9 more each time: every triangle in these pictures is equilateral, so each of its three angles is 60° — acute. Joining the midpoints of one small triangle replaces it by 4 smaller ones, that is 3 extra triangles, and each brings 3 more acute angles:
3 × 3 = 9 new acute angles
So the number of acute angles is always 3 × (number of small triangles): 3 × 1, 3 × 4, 3 × 7, 3 × 10 …