NCERT Solutions Ganita Prakash (Part 1) Chapter 5 Figure it Out — Across the Line
Book page 108 Updated on2026-09-05
Q1.
List all the linear pairs and vertically opposite angles you observe in Fig. 5.3: Linear Pairs — ∠a and ∠b, … ; Pairs of Vertically Opposite Angles — ∠b and ∠d, …
Answer
In Fig. 5.3 the lines l and m cross once, giving ∠a on the left, ∠b at the top, ∠c on the right and ∠d at the bottom.
Linear Pairs
Pairs of Vertically Opposite Angles
∠a and ∠b ∠b and ∠c ∠c and ∠d ∠d and ∠a
∠a and ∠c ∠b and ∠d
So there are 4 linear pairs and 2 pairs of vertically opposite angles.
Lines l and m crossing. ∠a and ∠c (blue) face each other, and so do ∠b and ∠d (red). Any two angles side by side, such as ∠a and ∠b, form a linear pair.
Why it happens: Walk once around the crossing point. Each neighbouring pair of angles lies on one straight line, so each neighbouring pair is a linear pair — that gives 4 of them. The angles that are not neighbours are the facing ones, and there are only 2 such pairs.
Tip: Every vertically opposite pair here is equal: ∠a = ∠c and ∠b = ∠d. Every linear pair adds to 180°.