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WAEC Mathematics 2012 Question 41

Question 41

Circle Theorems

The diagram is a circle with centre O. PRST are points on the circle. Find the value of ∠PRS.

Diagram for this question
  1. A.144°
  2. B.72°
  3. C.40°
  4. D.36°
Show the answer and explanation

Answer: A (144°)

Explanation

∠PTS = x stands on the arc PRS, so x = ½(360° − 8x), giving x = 36°. ∠PRS stands on the arc PTS, so ∠PRS = ½ × 8x = 4 × 36° = 144°.