JAMB 1983 · UME · Q26

If $O$ is the centre of the circle in the figure, find the value of $x$ .

Worked solution (try it first)

$C$ is on the minor arc, so $\angle ACB = 130^\circ$ stands on the major arc $AB$ .
The angle at the centre is twice the angle at the circumference, so the reflex angle $AOB$ is $2 \times 130^\circ = 260^\circ$ .
Angles at a point add up to $360^\circ$ , so $x = 360^\circ - 260^\circ = 100^\circ$ , option C.