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WAEC Mathematics 2013 Question 19

Question 19

Circle Theorems

In the diagram, VX is a tangent to the circle UYW at W. If WY//UV, ∠UYW = 95° and ∠UWY = 46°, find ∠UVW.

Diagram for this question
  1. A.51°
  2. B.49°
  3. C.39°
  4. D.34°
Show the answer and explanation

Answer: C (39°)

Explanation

WY ∥ UV gives ∠VUW = ∠UWY = 46° (alternate). The angle between tangent WV and chord WU equals the angle in the alternate segment: ∠UWV = 95°. So ∠UVW = 180° − 46° − 95° = 39°.