WAEC 2020 · Paper 1 · Q33

In the diagram, $O$ is the centre of the circle and $RP$ is a diameter. If $\angle OPQ = 48^\circ$ , find the value of $m$ .

Worked solution (try it first)

$OP = OQ$ (radii), so triangle $OPQ$ is isosceles and $\angle OQP = \angle OPQ = 48^\circ$ .
$ROP$ is a straight line, so $m = \angle ROQ$ is an exterior angle of triangle $OPQ$ .
An exterior angle equals the sum of the two interior opposite angles: $m = 48^\circ + 48^\circ = 96^\circ$ , option A.