Question

In the given figure, two chords PQ and RS intersects each other at A and SQ is perpendicular to RQ. If ∠PAR – ∠PSR = 30°, then find the value of ∠ASQ?

• A. 50°
• B. 55°
• C. 65°
• D. 60°

Answer 1

Answer:

D. 60°

Given, ∠PAR – ∠PSR = 30° ∵ ∠PAR = ∠SAQ (vertically opposite angles) And, ∠PSR = ∠PQR (drawn from same base PR) ∠SAQ – ∠PQR = 30° ⇒ ∠SAQ = 30° + ∠PQR ∵ SQ is perpendicular to RQ. ∴ ∠SQR = 90° ∴ ∠SQA = ∠SQR – ∠PQR = 90° – ∠PQR Now, ∠ASQ = 180° – ∠SAQ – ∠SQA ∠ASQ = 180° – (30° + ∠PQR) – (90° – ∠PQR) ∠ASQ = 180° – 30° – ∠PQR – 90° + ∠PQR ∠ASQ = 60°