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WAEC Mathematics 2001 Question 39

Question 39

Circle Theorems

In the diagram, PQ is a diameter of the circle and ∠PRS = 58°. Find ∠STQ.

Diagram for this question
  1. A.29°
  2. B.32°
  3. C.42°
  4. D.53°
Show the answer and explanation

Answer: B (32°)

Explanation

∠PQS = ∠PRS = 58° (same arc PS) and ∠PSQ = 90° (semicircle), so ∠SPQ = 32°. ∠STQ = ∠SPQ (same arc SQ) = 32°.