NECO 2022 · Paper 1 · Q34

Find the value of $k$ in the figure, where $O$ is the centre of the circle.

Worked solution (try it first)

The quadrilateral has all four vertices on the circle, so it is cyclic.
Opposite angles of a cyclic quadrilateral add up to $180^\circ$ : $k + 3k = 180^\circ$ .
So $4k = 180^\circ$ and $k = 45^\circ$ , option C.