NECO 2022 · Paper 1 · Q44

In the figure, $O$ is the centre of the circle. Find $\angle CAF$ .

Worked solution (try it first)

$ACBE$ is a cyclic quadrilateral, so opposite angles add up to $180^\circ$ : $\angle ACB = 180^\circ - 120^\circ$
$= 60^\circ$ .
Angles on a straight line add up to $180^\circ$ , so $\angle AFC = 180^\circ - 100^\circ$
$= 80^\circ$ .
The angles of triangle $ACF$ add up to $180^\circ$ : $\angle CAF = 180^\circ - 60^\circ - 80^\circ$
$= 40^\circ$ , option B.