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WAEC Mathematics 2013 Question 21

Question 21

Triangles and Quadrilaterals

In the diagram, PQRS is a rhombus and ∠PSQ = 35°. Calculate the size of ∠PRQ.

Diagram for this question
  1. A.65°
  2. B.55°
  3. C.45°
  4. D.35°
Show the answer and explanation

Answer: B (55°)

Explanation

The diagonals cross at right angles, so in the small triangle at P, ∠SPR = 180° − 90° − 35° = 55°. PS ∥ QR, so ∠PRQ = ∠SPR = 55° (alternate angles).