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WAEC Mathematics 2024 Question 31

Question 31

Circle Theorems

In the diagram, JKL is a tangent to the circle GHIK at K. ∠LKG = 38° and ∠HIK = 87°. Calculate the value of the angle marked x.

Diagram for this question
  1. A.93°
  2. B.55°
  3. C.42°
  4. D.23°
Show the answer and explanation

Answer: B (55°)

Explanation

The exterior angle KGL of the cyclic quadrilateral GHIK equals the opposite interior angle HIK = 87°. In triangle GKL, x = 180° − 87° − 38° = 55°.