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WAEC Mathematics 1988 Question 41

Question 41

Circle Theorems

In the diagram below, O is the centre of the circle through points L, M and N, if ∠MLN = 74° and ∠MNL = 39°, calculate ∠LON.

Diagram for this question
  1. A.67°
  2. B.100°
  3. C.113°
  4. D.126°
  5. E.134°
Show the answer and explanation

Answer: E (134°)

Explanation

∠LMN = 180° − 74° − 39° = 67°. The angle at the centre is twice the angle at the circumference on the same arc, so ∠LON = 2 × 67° = 134°.