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WAEC Mathematics 2023 Question 37

Question 37

Circle Theorems

In the diagram, O is the centre of the circle QRS and ∠SQR = 28°. Find ∠ORS.

Diagram for this question
  1. A.76°
  2. B.62°
  3. C.56°
  4. D.28°
Show the answer and explanation

Answer: B (62°)

Explanation

The angle at the centre is twice the angle at the circumference: ∠SOR = 56°. Triangle SOR is isosceles (OS = OR), so ∠ORS = (180° − 56°)/2 = 62°.