In △PQR, S is a point on the side QR such that ∠QPS = 1/2 ∠PSR, ∠QPR = 78º and ∠PRS = 44º. What is the measure of ∠PSQ?

In △PQR, S is a point on the side QR such that ∠QPS = 1/2…

In △PQR, S is a point on the side QR such that ∠QPS = $\frac{1}{2}$ ∠PSR, ∠QPR = 78º and ∠PRS = 44º. What is the measure of ∠PSQ?

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 64º

∠QPR = 78º

∠SPR = 78º - $\frac{\theta}{2}$

By using the triangle sum property in △PSR,

∠SPR + ∠PSR + ∠PRS = 180°

78º - $\frac{\theta}{2}$ + $\theta$ + 44 = 180

$\theta$ = 116

∠PSR + ∠PSQ = 180 ( linear pair)

∠PSQ = 180 - 116 = 64°.