WAEC 2024 · Paper 1 · Q38

Find the value of $x$ in the diagram.

The paper marks this diagram “not drawn to scale”; the redraw uses the true measurements.

Worked solution (try it first)

$QR \parallel MP$ , so $\angle NRQ = \angle NPM = 55^\circ$ (corresponding angles).
The angles of triangle $NQR$ add up to $180^\circ$ : $\angle NQR = 180^\circ - 65^\circ - 55^\circ$
$= 60^\circ$ .
$MQN$ is a straight line, so $x = \angle MQR$
$= 180^\circ - 60^\circ$
$= 120^\circ$ , option C.