JAMB 1983 · UME · Q41

In the figure, $O$ is the centre of the circle and the reflex angle $POQ$ is $235^\circ$ . Find $\angle PRQ$ .

Worked solution (try it first)

Angles at a point add up to $360^\circ$ , so the non-reflex angle $POQ$ is $360^\circ - 235^\circ = 125^\circ$ .
$R$ is on the major arc, so $\angle PRQ$ stands on the minor arc $PQ$ , the same arc as the $125^\circ$ at $O$ .
The angle at the circumference is half the angle at the centre: $\angle PRQ = \frac12 \times 125^\circ$
$= 62\frac12^\circ$ , option B.