NCERT Solutions Ganita Prakash Chapter 2 Figure it Out — Types of Angles and their Measures
Book page 51 & 52 Updated on2026-09-05
Q1.
In each of the below grids, join A to other grid points in the figure by a straight line to get: a. An acute angle b. An obtuse angle c. A reflex angle. Mark the intended angles with curves to specify the angles. One has been done for you.
Answer
In each part the red segment AB is already drawn — that is the fixed arm. You only have to join A to one more grid point so that the second arm makes the angle asked for. Both grids of a part are done the same way; in the first grid AB is horizontal, in the second it slants 2 steps right and 2 steps down.
Two of the grids of page 51–52. The red segment AB is already given; joining A to a further grid point makes the required angle.
Wanted angle
Grid with AB horizontal
Grid with AB slanting
a. Acute (less than 90°)
join A to a point above the line and towards B — 2 right, 2 up gives 45°
join A to a point just above the slant — 2 right, 0 up gives 45°
b. Obtuse (between 90° and 180°)
join A to a point above the line but on the far side of A — 2 left, 2 up gives 135°
join A straight up — 0 right, 2 up gives 135°
c. Reflex (more than 180°)
join A to a point below the line — 2 left, 2 down — and draw the curve the long way round: 225°
join A 2 left, 0 down and mark the curve the long way round: 225°
The trick for the reflex angle: the same two arms make two angles — a small one and a big one that together add to 360°. Draw the curve on the outer side to show that you mean the big one: 360° − 135° = 225°.
Tip: on a square grid, going the same number of steps across as up gives 45°, and turning that direction by a quarter turn gives 135° — so all three kinds of angle can be made without a protractor.
Q2.
Use a protractor to find the measure of each angle. Then classify each angle as acute, obtuse, right, or reflex. a. ∠PTR b. ∠PTQ c. ∠PTW d. ∠WTP
Answer
The rays TP, TR, TQ and TW of page 52, measured on the page: ∠PTR = 30°, ∠PTQ = 60°, ∠PTW = 102°.
The vertex is T. Keep TP as the base arm and read each of the other arms from it:
Angle
Measure
Type
a. ∠PTR
30°
acute
b. ∠PTQ
60°
acute
c. ∠PTW
102°
obtuse
d. ∠WTP
258°
reflex
Why (c) and (d) are different: the same two arms TP and TW bound two angles — the one you go through one way and the one you go through the other way. The book marks the smaller one as ∠PTW and the bigger one as ∠WTP.
Tip: a reflex angle is never read directly — measure the smaller angle first and subtract from 360°. (Measured exactly, the printed figure gives 30.3°, 59.3°, 102.7° and 257.3°.)