WAEC Mathematics 2023 Paper

Concept:The angle at the centre is twice the angle at the circumference for the same arc, and the sum of interior angles of a quadrilateral is $360^\circ$.Explanation:Given $\angle RNM = 124^\circ$, the reflex angle at the centre subtending the same arc $RM$ is $2 \times 124^\circ = 248^\circ$.Therefore, the smaller central angle is $\angle MOR = 360^\circ - 248^\circ = 112^\circ$.Consider quadrilateral $MORN$. Its interior angles are $\angle OMN$, $\angle MOR$, $\angle ORN$, and $\angle RNM$.Thus, $\angle OMN + 112^\circ + 48^\circ + 124^\circ = 360^\circ$.So, $\angle OMN = 360^\circ - 284^\circ = 76^\circ$.Answer:$\angle OMN = 76^\circ$, which is option D.