WAEC 2021 · Paper 1 · Q29

In the diagram, $O$ is the centre of the circle, $\angle PQR = 72^\circ$ and $OR$ is parallel to $PS$ . Find $\angle OPS$ .

Worked solution (try it first)

$\angle POR$ is at the centre on the same arc $PR$ as $\angle PQR$ at the circumference.
So $\angle POR = 2 \times 72^\circ$
$= 144^\circ$ .
$OR \parallel PS$ , so $\angle OPS$ and $\angle POR$ are co-interior angles and add up to $180^\circ$ .
So $\angle OPS = 180^\circ - 144^\circ$
$= 36^\circ$ , option D.