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WAEC Mathematics 2021 Question 30

Question 30

Circle Theorems

In the diagram, O is the centre of circle PQRS, ∠PQR = 72° and OR ∥ PS. Find ∠OPS.

Diagram for this question
  1. A.18°
  2. B.108°
  3. C.54°
  4. D.36°
Show the answer and explanation

Answer: D (36°)

Explanation

∠POR = 2 × 72° = 144°, so in isosceles triangle OPR, ∠OPR = ∠ORP = 18°. ∠RPS = ∠ORP = 18° (alternate angles), so ∠OPS = 18° + 18° = 36°.