NECO 2023 · Paper 1 · Q35

In the diagram, $O$ is the centre of the circle $PQR$ . If $\angle QPR = 64^\circ$ and $\angle QRP = 46^\circ$ , calculate $\angle POQ$ .

Worked solution (try it first)

$\angle POQ$ is at the centre on arc $PQ$ .
The angle at the circumference on the same arc is at $R$ : $\angle PRQ = 46^\circ$ .
The angle at the centre is twice the angle at the circumference: $\angle POQ = 2 \times 46^\circ = 92^\circ$ , option C.