Multiple choice

PQ is a diameter of the circle and PR is a chord of a circle such that ∠QPR =300. The tangent at R intersects PQ produced in S. Then ∠RQS = ? PQ वृत्त का व्यास है और PR वृत्त पर एक जीवा है ताकि ∠QPR = 300 बिन्दु R पर स्पर्श रेखा PR को बढ़ाने पर बिन्दु S पर प्रतिच्छेद करती है। तो ∠RQS

  1. 600

  2. 900

  3. 300

  4. 1200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

PQ is a diameter, so ∠PRQ = 90° (angle in semicircle). Given ∠QPR = 30°, then ∠PQR = 60°. By alternate segment theorem, ∠PRS = ∠PQR = 60°. In cyclic quadrilateral PQRS, opposite angles sum to 180°, so ∠RQS = 180° - 60° = 120°.

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