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

Solution (By Examveda Team)

∠QPS = $$\frac{1}{2}$$∠PSR = x (Let)
∠PSR = 2x
∠PQS + ∠QPS = 2x
∠QPR = 78° and ∠PRS = 44°

In ΔPQR
∠P + ∠Q + ∠R = 180°
78° + x + 44° = 180°
x = 180° - 122°
x = 58°
∠PSQ = 180° - 2x
= 180° - 2 × 58°
= 180° - 116°
= 64°