WAEC Mathematics 2015 Objective — Question 16

Question 16 of 50 from the West African Examinations Council (WAEC) Mathematics 2015 Objective paper, with the correct answer and a full explanation.

In the diagram above, O is the centre of the circle. If PQ//RS and ∠ONS = 140°, find the size of ∠POM.

• A. 40°Correct
• B. 50°
• C. 60°
• D. 80°

Explanation

∠ONM = 180−140 = 40° (angles on a straight line). Since OM=ON (radii), triangle OMN is isosceles so ∠NMO=40°, and since PQ//RS, ∠POM = ∠NMO = 40° (alternate angles).

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