WAEC 2020 · Paper 1 · Q44

In the diagram, $O$ is the centre of the circle. If $\angle NLM = 74^\circ$ , $\angle LMN = 39^\circ$ and $\angle LOM = x$ , find the value of $x$ .

Worked solution (try it first)

The angles of triangle $LMN$ add up to $180^\circ$ : $\angle LNM = 180^\circ - 74^\circ - 39^\circ$
$= 67^\circ$ .
$\angle LNM$ is at the circumference on arc $LM$ , the same arc as $x$ at the centre.
The angle at the centre is twice the angle at the circumference: $x = 2 \times 67^\circ = 134^\circ$ , option A.