Question

In ΔPQR, ∠Q = 90°, ∠P = 40°, RS bisects ∠PRQ.

∴ find x.

Options

• 20°

• 25°

• 70°

• 65°

Answer 1

65°

Explanation:

1. Given:

∠Q = 90°  ...(Right angle)

∠P = 40°

Therefore, ∠R = 180° – ∠P – ∠Q

= 180° – 40° – 90°

= 50°

2. RS bisects ∠PRQ:

Since RS is the angle bisector of ∠R = 50°, it divides ∠R into two equal parts:

`x = 50^circ/2`

= 25°

However, we need to find the angle ∠RPS i.e., ∠PRS + ∠P.

Since x = 25° half of ∠R and ∠P = 40°:

∠RPS = ∠P + ∠PRS

= 40° + 25°

= 65°