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WAEC Mathematics 2021 Question 35

Question 35

Circle Theorems

In the diagram, MP is a tangent to the circle NQR, ∠PNQ = 64° and |RQ| = |RN|. Find the angle marked t.

Diagram for this question
  1. A.130°
  2. B.115°
  3. C.58°
  4. D.64°
Show the answer and explanation

Answer: C (58°)

Explanation

By the alternate segment theorem ∠NRQ = 64°. Triangle RQN is isosceles, so ∠RQN = (180° − 64°)/2 = 58°, and t = ∠RQN = 58° (alternate segment again).