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Angle subtended by chord in circle

CMAT 2018 · Quantitative Techniques & Data Interpretation · Medium · Geometry

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In the figure, PQ is a diameter of the circle. Angle PQS = 35∘35^\circ. Find angle QRS.

  1. A.

    55∘55^\circ

  2. B.

    45∘45^\circ

  3. C.

    35∘35^\circ

  4. D.

    60∘60^\circ

Answer

A

Explanation

Since PQ is the diameter, ∠PSQ=90∘\angle PSQ = 90^\circ (angle in a semicircle). In △PSQ\triangle PSQ, ∠QPS=180∘−90∘−35∘=55∘\angle QPS = 180^\circ - 90^\circ - 35^\circ = 55^\circ. Since angles subtended by chord QS in the same segment are equal: ∠QRS=∠QPS=55∘.\angle QRS = \angle QPS = 55^\circ.

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