WAEC 2024 · Paper 1 · Q30

In the diagram, $\angle SQR = 52^\circ$ and $\angle PRT = 16^\circ$ . Find the value of the angle marked $y$ .

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

Worked solution (try it first)

$PQST$ is a cyclic quadrilateral.
Its exterior angle at $Q$ , $\angle SQR$ , equals the interior opposite angle at $T$ : $\angle PTS = 52^\circ$ .
The angles of triangle $PRT$ add up to $180^\circ$ : $y = 180^\circ - 52^\circ - 16^\circ$
$= 112^\circ$ , option C.