WAEC 2023 · Paper 1 · Q46

In the diagram, $M$ , $N$ , $R$ are points on the circle centre $O$ ; $\angle ORN = 48^\circ$ and $\angle RNM = 124^\circ$ . Find $\angle OMN$ .

Worked solution (try it first)

$\angle MNR = 124^\circ$ stands on the major arc $MR$ , so the reflex angle $MOR$ is $2 \times 124^\circ = 248^\circ$ .
So the angle $MOR$ inside quadrilateral $OMNR$ is $360^\circ - 248^\circ = 112^\circ$ .
The angles of a quadrilateral add up to $360^\circ$ : $\angle OMN = 360^\circ - 124^\circ - 48^\circ - 112^\circ$
$= 76^\circ$ , option A.