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WAEC Mathematics 2008 Question 44

Question 44

Circle Theorems

In the diagram, PX is a tangent to the circle and RST is an equilateral triangle. Calculate ∠PTS.

Diagram for this question
  1. A.60°
  2. B.90°
  3. C.120°
  4. D.150°
Show the answer and explanation

Answer: C (120°)

Explanation

By the alternate segment theorem, ∠STX = ∠TRS = 60°. P, T, X lie on a straight line, so ∠PTS = 180° − 60° = 120°.