WAEC 2019 · Paper 1 · Q30

In the diagram, $POS$ and $ROT$ are straight lines, $OPQR$ is a parallelogram, $|OS| = |OT|$ and $\angle OST = 50^\circ$ . Calculate $\angle OPQ$ .

Worked solution (try it first)

$|OS| = |OT|$ , so both base angles of triangle $OST$ are $50^\circ$ and $\angle SOT = 180^\circ - 100^\circ$
$= 80^\circ$ .
$POS$ and $ROT$ are straight lines, so $\angle POR = \angle SOT = 80^\circ$ (vertically opposite).
In the parallelogram $OR \parallel PQ$ , so $\angle OPQ$ and $\angle POR$ are co-interior: $\angle OPQ = 180^\circ - 80^\circ$
$= 100^\circ$ , option A.