WAEC Mathematics 2014 Objective — Question 32

Question 32 of 50 from the West African Examinations Council (WAEC) Mathematics 2014 Objective paper, with the correct answer and a full explanation.

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°.

• A. 2x°
• B. (90−x)°
• C. (90+x)°
• D. (180−2x)°Correct

Explanation

∠TRQ=∠UTR=x° (alternate angles, since UT∥PQ). Also ∠TRQ=∠TUR=x° (angles in alternate segment). In triangle TUR: ∠TUR+∠UTR+∠URT=180°, so ∠URT=180°−2x°.

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