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WAEC Mathematics 1999 Question 50

Question 50

Circle Theorems

In the diagram, CDE is a triangle, ABEF is cyclic quadrilateral, AB || CD, ∠BAF = 65° and ∠AFE = 85°. Calculate ∠CDE

Diagram for this question
  1. A.20°
  2. B.30°
  3. C.50°
  4. D.65°
Show the answer and explanation

Answer: B (30°)

Explanation

Opposite angles of ABEF: ∠ABE = 95° and ∠BEF = 115°, so ∠CED = 65° and ∠ABC = 85°. AB ∥ CD gives ∠BCD = 85°, so ∠CDE = 180 − 85 − 65 = 30°.