WAEC Mathematics 2023 Objective — Question 46

Question 46 of 50 from the West African Examinations Council (WAEC) Mathematics 2023 Objective paper, with the correct answer and a full explanation.

In the diagram, M, N, R are points on the circle centre O. ∠ORN=48° and ∠RNM=124°. Find ∠OMN.

• A. 76°Correct
• B. 64°
• C. 58°
• D. 76°

Explanation

∠MOR(reflex)=2×∠MNR=248°, so ∠MOR(obtuse)=360-248=112°. In quadrilateral OMN R (sum of angles): ∠OMN+124+112+48=360 → ∠OMN=360-284=76°.

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