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WAEC Mathematics 2015 Question 16

Question 16

Circle Theorems

In the diagram, O is the centre of the circle. If PQ//RS and ∠ONS = 140°, find the size of ∠POM.

Diagram for this question
  1. A.40°
  2. B.50°
  3. C.60°
  4. D.80°
Show the answer and explanation

Answer: A (40°)

Explanation

∠ONM = 180° − 140° = 40°. OM = ON (radii), so ∠OMN = 40°, and ∠POM = ∠OMN = 40° (alternate angles, PQ//RS).