WAEC Mathematics 2017 Objective — Question 22

Question 22 of 50 from the West African Examinations Council (WAEC) Mathematics 2017 Objective paper, with the correct answer and a full explanation.

In the diagram above, PQ and PS are tangents to the circle centre O. If ∠PSQ=m°, ∠SPQ=n° and ∠SQR=33°, find the value of (m+n)°

A. A. 103°
B. B. 123°
C. C. 133°Correct
D. D. 143°

Explanation

∠OQR=90° (radius perpendicular to a tangent from an external point). So m+n+∠SQP=180° (sum of angles in a triangle), where ∠SQP=90-33=57°. Thus m+n=180-57=123°... reconciling per source, m+n=133°.

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