WAEC Mathematics 2016 Objective — Question 22

Question 22 of 50 from the West African Examinations Council (WAEC) Mathematics 2016 Objective paper, with the correct answer and a full explanation.

22. In the diagram, TS is a tangent to the circle at S. |PR| and ∠PQR=117°. Calculate ∠PST. A. 54° B. 44° C. 34° D. 27°

• A. 54°Correct
• B. 44°
• C. 34°
• D. 27°

Explanation

∠PRS=180-117=63° (opposite angles of cyclic quadrilateral); ∠RPS=63°(base angles of isosceles Δ); ∠PRS(final)=180-2(63)=54°; ∠PST=∠PRS=54° (angles in alternate segment).

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