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JAMB Mathematics 2000 Question 29

Question 29

Triangles and Quadrilaterals

In the diagram above, if ∠RPS = 50°, ∠RPQ = 30° and PQ = QR, find the value of ∠PRS.

Diagram for this question
  1. A.80°
  2. B.70°
  3. C.60°
  4. D.50°
Show the answer and explanation

Answer: B (70°)

Explanation

Since PQ = QR, ∠QRP = 30° and ∠PQR = 120°. Opposite angles of a cyclic quadrilateral add to 180°, so ∠PSR = 60°. In triangle PRS, ∠PRS = 180° − 50° − 60° = 70°.