In a △PQR, PQ = PR and QP produced to S such that PQ = PS. Find angle ∠QRS.
(A) 90^°
(B) 75^°
(C) 65^°
(D) 60^°


Answer: (A)

Explanation:

∠Q = ∠R = Θ

∠RPS = ∠Q + ∠R = 2Θ (Exterior angles always equals to sum of opposite interior angles)

△PSR is an isosceles triangle.

∠PRS + ∠PSR + ∠P = 180^°

∠PRS = ∠PSR

2∠PRS = 180^° – 2Θ

∠PRS = 90^° – Θ

∠QRS = Θ + 90^° – Θ

∠QRS = 90^°

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