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WAEC Mathematics 1999 Question 48

Question 48

Circle Theorems

In the diagram, O is the centre of the circle. ∠PQR = 75°, ∠OPS = y° and OR is parallel to PS. Find y.

Diagram for this question
  1. A.15
  2. B.30
  3. C.45
  4. D.75.
Show the answer and explanation

Answer: B (30)

Explanation

∠POR = 2 × 75° = 150° (angle at centre). OR ∥ PS, so ∠OPS and ∠POR are co-interior: y = 180 − 150 = 30.