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WAEC Mathematics 1988 Question 36

Question 36

Angles and Polygons

In the diagram below, LK//PQ, reflex angle KLM = 241° and ∠QPM = 89°. What is the value of ∠LMP?

Diagram for this question
  1. A.30°
  2. B.61°
  3. C.89°
  4. D.119°
  5. E.150°
Show the answer and explanation

Answer: A (30°)

Explanation

Draw a line through M parallel to KL. ∠KLM = 360° − 241° = 119°, so the angle between ML and that line is 180° − 119° = 61°. The angle between MP and that line is 180° − 89° = 91° (co-interior with PQ). So ∠LMP = 91° − 61° = 30°.