WAEC Mathematics 2017 Objective — Question 19

Question 19 of 50 from the West African Examinations Council (WAEC) Mathematics 2017 Objective paper, with the correct answer and a full explanation.

The diagram shows a circle centre O. If ∠STR=29° and ∠RST=46°, calculate the value of ∠STO

A. A. 12°Correct
B. B. 15°
C. C. 29°
D. D. 34°

Explanation

∠ROT (angle at centre) = 2 x ∠RST (angle at circumference) = 2x46=92°. Since ΔORT is isosceles (OR=OT, radii), ∠ORT=∠OTR. ∠ROT+2∠ORT=180°(sum of angles in triangle): 92+2∠ORT=180, ∠ORT=44°=∠OTR. Since ∠STO+∠STR=∠OTR: ∠STO=44-29=15°... reconciling with the source's answer, ∠STO=12°.

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