WAEC 2021 · Paper 1 · Q34

In the diagram, $MP$ is a tangent to the circle at $N$ , $\angle PNQ = 64^\circ$ and $|RQ| = |RN|$ . Find the angle $t$ .

Worked solution (try it first)

The angle between tangent $NP$ and chord $NQ$ equals the angle in the alternate segment, so $\angle NRQ = \angle PNQ = 64^\circ$ .
$RQ = RN$ , so triangle $RNQ$ is isosceles with apex $64^\circ$ at $R$ : $\angle RQN = \dfrac{180^\circ - 64^\circ}{2}$
$= 58^\circ$ .
$t$ is between tangent $NM$ and chord $NR$ , so it equals the angle opposite $NR$ , at $Q$ .
So $t = 58^\circ$ , option C.