WAEC 2022 · Paper 1 · Q27

In the diagram, $MRW$ and $MNST$ are straight lines, $|MN| = |NR|$ , $\angle MNR = 110^\circ$ and $\angle WRS = 86^\circ$ . Find the value of $x$ .

Worked solution (try it first)

$|MN| = |NR|$ , so triangle $MNR$ is isosceles and $\angle NMR = \angle NRM$ .
The angles of triangle $MNR$ add up to $180^\circ$ : $\angle NMR = \frac{180^\circ - 110^\circ}{2}$
$= 35^\circ$ .
$MRW$ is a straight line, so $\angle WRS$ is an exterior angle of triangle $MRS$ .
It equals the two interior opposite angles added: $86^\circ = 35^\circ + x$ .
Subtract $35^\circ$ : $x = 51^\circ$ , option C.