WAEC Mathematics 2025 Objective — Question 36

Question 36 of 51 from the West African Examinations Council (WAEC) Mathematics 2025 Objective paper, with the correct answer and a full explanation.

In the diagram, O is the centre of the circle. SOQ is the diameter and angle SRP = 37 deg. Find angle PSQ.

A. 127 deg
B. 65 deg
C. 53 degCorrect
D. 37 deg

Explanation

Angle SRP and angle SQP are angles on the same segment subtending arc SP, so angle SQP=37 deg. Angle PSQ+90+37=180 (angle in a semicircle is 90 deg, angles in a triangle sum to 180), giving angle PSQ=180-127=53 deg.

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