The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of ∠PSR is

A. 30°

B. 15°

C. 60°

D. 45°

Answer: Option A

Solution(By Examveda Team)

According to question,
Given :

PQR is an equilateral triangle
QR = RS
PR = RS
∠SRP = 180° - 60° (Exterior ∠)
∠SRP = 120°
∴ ∠RPS = ∠RSP
∴ ∠RPS + ∠PRS + ∠RSP = 180°
2∠PSR = 180° - 120°
∠PSR = $$\frac{{{{60}^ \circ }}}{2}$$
∠PSR = 30°