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WAEC Mathematics 2011 Question 23

Question 23

Angles and Polygons

In the diagram, MN//OP, ∠NMQ = 65° and ∠QOP = 125°. What is the size of ∠MQR?

Diagram for this question
  1. A.110°
  2. B.120°
  3. C.130°
  4. D.160°
Show the answer and explanation

Answer: B (120°)

Explanation

∠NOP = 180° − 125° = 55°, and MN ∥ OP gives ∠MNQ = 55° (alternate). In ΔMNQ, ∠MQN = 180° − 65° − 55° = 60°. NQR is a straight line, so ∠MQR = 180° − 60° = 120°.