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GCE Mathematics 1990 Question 31

Question 31

Triangles and Quadrilaterals

In the diagram below, WXYZ is a rhombus and ∠WYX = 20°. What is the value of ∠XZY?

Diagram for this question
  1. A.20°
  2. B.30°
  3. C.45°
  4. D.60°
  5. E.70°
Show the answer and explanation

Answer: E (70°)

Explanation

A diagonal of a rhombus bisects its angles, so ∠XYZ = 40°. Triangle XYZ is isosceles (YX = YZ), so ∠XZY = (180° − 40°)/2 = 70°.