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JAMB Mathematics 1987 Question 35

Question 35

Circle Theorems

Two chords QR and NP of a circle intersect inside the circle at X. If RQ̂P = 37°, RQ̂N = 49° and QP̂N = 35° find PR̂Q.

  1. A.35°
  2. B.37°
  3. C.49°
  4. D.59°
Show the answer and explanation

Answer: D (59°)

Explanation

In triangle PQN, angle PQN = 37° + 49° = 86° and angle QPN = 35°, so angle QNP = 180° − 121° = 59°. Angle PRQ stands on the same arc PQ as angle PNQ, so it is also 59°.