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WAEC Mathematics 2014 Question 32

Question 32

Circle Theorems

In the figure, PQ is a tangent to the circle at R and UT is parallel to PQ. If ∠TRQ = x°, find ∠URT in terms of x.

Diagram for this question
  1. A.2x°
  2. B.(90 − x)°
  3. C.(90 + x)°
  4. D.(180 − 2x)°
Show the answer and explanation

Answer: D ((180 − 2x)°)

Explanation

UT ∥ PQ gives ∠UTR = ∠TRQ = x (alternate). The alternate segment theorem gives ∠TUR = ∠TRQ = x. So ∠URT = 180° − 2x.