WAEC 2023 · Paper 1 · Q30

Circle geometry

In the diagram, $NR$ is a diameter, $SRM$ is a straight line, $\angle MNR = x^\circ$ and $\angle SRN = (5x + 20)^\circ$ . Find the value of $2x^\circ$ .

Worked solution (try it first)

$NR$ is a diameter, so $\angle NMR = 90^\circ$ .
In triangle $NMR$ , $\angle MRN = 180^\circ - 90^\circ - x^\circ$
$= (90 - x)^\circ$ .
$SRM$ is a straight line, so $\angle SRN + \angle MRN = 180^\circ$ : $(5x + 20) + (90 - x) = 180$ .
Simplify: $4x + 110 = 180$ , so $4x = 70$ and $x = 17.5$ .
So $2x = 35^\circ$ , option B.

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