WAEC 2022 · Paper 1 · Q30

In the diagram, $MNR$ is a tangent to the circle at $N$ and $\angle NOS = 108^\circ$ . Find $\angle OSN$ .

Worked solution (try it first)

$ON = OS$ (radii), so triangle $NOS$ is isosceles and its base angles at $N$ and $S$ are equal.
So $\angle OSN = \dfrac{180^\circ - 108^\circ}{2}$
$= 36^\circ$ , option C.
The tangent is not needed.