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WAEC Mathematics 2021 Question 40

Question 40

Circle Theorems

In the diagram, EC is a diameter of the circle ABCDE. If ∠ABC = 158°, find ∠ADE.

Diagram for this question
  1. A.112°
  2. B.90°
  3. C.68°
  4. D.22°
Show the answer and explanation

Answer: C (68°)

Explanation

ABCE is cyclic, so ∠AEC = 180° − 158° = 22°. ∠EAC = 90° (angle in a semicircle), so ∠ACE = 68°, and ∠ADE = ∠ACE = 68° (same segment).