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WAEC Mathematics 1988 Question 43

Question 43

Triangles and Quadrilaterals

In the diagram, PR is the perpendicular from P to QS, PQ = 2cm, QR = 1cm and PR = RS. What is the size of the angle QPS?

Diagram for this question
  1. A.135°
  2. B.105°
  3. C.90°
  4. D.75°
  5. E.60°
Show the answer and explanation

Answer: D (75°)

Explanation

In triangle PQR, sin ∠QPR = 1/2, so ∠QPR = 30°. Triangle PRS is right-angled and isosceles, so ∠RPS = 45°. ∠QPS = 30° + 45° = 75°.