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JAMB Mathematics 1984 Question 35

Question 35

Circle Theorems

In the figure above, QRS is a line, PSQ = 35°, SPR = 30° and O is the centre of the circle. Find OQP.

Diagram for this question
  1. A.35°
  2. B.30°
  3. C.130°
  4. D.25°
  5. E.65°.
Show the answer and explanation

Answer: D (25°)

Explanation

<PRQ is an exterior angle of triangle PRS: 35° + 30° = 65°. The angle at the centre <POQ = 130°, and triangle OPQ is isosceles, so <OQP = (180° − 130°)/2 = 25°.