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JAMB Mathematics 1991 Question 36

Question 36

Circle Theorems

Use the figure below to answer questions 35 and 36. PMN and PQR are two secants of the circle MQTRN and PT is a tangent.
If PN̂R = 110° and PM̂Q = 55°, find MP̂Q

Diagram for this question
  1. A.40°
  2. B.30°
  3. C.25°
  4. D.15°
Show the answer and explanation

Answer: D (15°)

Explanation

MQRN is cyclic, so the exterior angle PMQ equals the interior opposite angle QRN = 55°. In triangle PNR, angle P = 180° − 110° − 55° = 15°.