WAEC Mathematics 2017 Objective — Question 50

Question 50 of 50 from the West African Examinations Council (WAEC) Mathematics 2017 Objective paper, with the correct answer and a full explanation.

In the diagram, RP is a diameter of the circle RSP, RP is produced to T and TS is a tangent to the circle at S. If ∠PRS=24°, calculate the value of ∠STR.

A. A. 24°
B. B. 42°Correct
C. C. 48°
D. D. 66°

Explanation

∠PSR=90° (angle in a semicircle). ∠PST=∠PRS=24° (angle between tangent and chord equals angle in alternate segment). ∠RST=90+24=114°. From ΔRST: ∠PRS+∠RST+∠STR=180°, so ∠STR=180-(24+114)=42°.

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