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WAEC Mathematics 2002 Question 20

Question 20

Circle Theorems

In the diagram, SQ is a tangent to the circle at P, XP||YQ, ∠XPY = 56° and ∠PXY = 80°. Find angle PQY.

Diagram for this question
  1. A.24°
  2. B.36°
  3. C.44°
  4. D.46°
Show the answer and explanation

Answer: C (44°)

Explanation

In triangle PXY, ∠PYX = 180 − 56 − 80 = 44°. The tangent–chord angle ∠SPX equals ∠PYX = 44°, and XP ∥ YQ makes ∠PQY = ∠SPX = 44° (corresponding angles).