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WAEC Mathematics 1999 Question 17

Question 17

Triangles and Quadrilaterals

In the diagram below, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62°. Calculate ∠XYZ.

Diagram for this question
  1. A.50°
  2. B.62°
  3. C.112°
  4. D.115°
Show the answer and explanation

Answer: D (115°)

Explanation

Triangle XRY is isosceles with apex 62°, so ∠RYX = 59°. Triangle RYZ has RY = YZ, so ∠YZR = 62° and ∠RYZ = 56°. ∠XYZ = 59 + 56 = 115°.