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WAEC Mathematics 2016 Question 18

Question 18

Circle Theorems

In the diagram, YW is a tangent to the circle at X, |UV| = |VX| and ∠VXW = 50°. Find the value of ∠UXY

Diagram for this question
  1. A.70°
  2. B.80°
  3. C.105°
  4. D.110°
Show the answer and explanation

Answer: B (80°)

Explanation

∠VUX = ∠VXW = 50° (alternate segment). Triangle UVX is isosceles, so ∠UXV = 50° and ∠UVX = 80°; by the alternate segment theorem ∠UXY = ∠UVX = 80°.