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JAMB Mathematics 1989 Question 35

Question 35

Angles and Polygons

In the above diagram PQ is parallel to RS and QS bisects PQ̂R. If PR̂Q is 60°, find x

Diagram for this question
  1. A.30°
  2. B.40°
  3. C.60°
  4. D.120°
Show the answer and explanation

Answer: B (40°)

Explanation

Angle PRQ = 60° means arc PQ = 120°. QS bisects angle PQR, so arcs PS and SR are equal, and the parallel chords make arc QR equal to arc PS. These three equal arcs share 240°, so each is 80°. x stands on arc QR, so x = 40°.