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WAEC Mathematics 2016 Question 41

Question 41

Circle Theorems

In the diagram, O is the centre of the circle, ∠QPS = 100°, ∠PSQ = 60° and ∠QSR = 80°. Calculate ∠SQR.

Diagram for this question
  1. A.20°
  2. B.40°
  3. C.60°
  4. D.80°
Show the answer and explanation

Answer: A (20°)

Explanation

∠QRS = 180° − 100° = 80° (opposite angles of cyclic quadrilateral). In triangle QRS, ∠SQR = 180° − 80° − 80° = 20°.