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WAEC Mathematics 1998 Question 35

Question 35

Circle Theorems

In the diagram PQ is a diameter of circle PMQN centre O. If ∠PQM = 63°, find ∠MNQ.

Diagram for this question
  1. A.58.5°
  2. B.44°
  3. C.35°
  4. D.31.5°
  5. E.27°.
Show the answer and explanation

Answer: E (27°.)

Explanation

∠PMQ = 90° (angle in a semicircle), so ∠MPQ = 27°. ∠MNQ = ∠MPQ (same arc MQ) = 27°.