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JAMB Mathematics 1983 Question 47

Question 47

Angles and Polygons

In the above diagram, if PS = SR and PQ∥SR, what is the size of PQR?

Diagram for this question
  1. A.25°
  2. B.50°
  3. C.55°
  4. D.65°
  5. E.75°.
Show the answer and explanation

Answer: C (55°)

Explanation

Triangle PSR is isosceles with <S = 130°, so <SRP = 25°, and <RPQ = 25° (alternate angles, PQ ∥ SR). In triangle PQR with <PRQ = 100°, <PQR = 180° − 100° − 25° = 55°.