WAEC 2022 · Paper 1 · Q36

Circle geometry

In the diagram, triangle $MNR$ is inscribed in circle $MNR$ and $PQ$ is a straight line. If $\angle MRN = 41^\circ$ and $\angle PMR = 141^\circ$ , find $\angle QNR$ .

Worked solution (try it first)

$PMNQ$ is a straight line: $\angle RMN = 180^\circ - 141^\circ$
$= 39^\circ$ .
$\angle QNR$ is an exterior angle of triangle $MNR$ , so it equals the sum of the two interior opposite angles.
So $\angle QNR = 39^\circ + 41^\circ$
$= 80^\circ$ , option B.

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