waecmaths question:
In the diagram, O is the centre of the circle If PQ $PQ\parallel RS$and $\angle ONS={{140}^{\circ }}$find the size of $\angle POM$
Option A:
40o
Option B:
50o
Option C:
60o
Option D:
80o
waecmaths solution:
$\begin{align} & \angle MNO={{180}^{\circ }}-\angle ONS\text{ }\!\!\{\!\!\text{ Sum of }\angle s\text{ on a straight line }\!\!\}\!\!\text{ } \\ & \angle MNO={{180}^{\circ }}-{{140}^{\circ }}={{40}^{\circ }} \\ & \left| ON \right|=\left| OM \right|\text{ }\!\!\{\!\!\text{ Radius of circle} \\ & \angle OMN=\angle NMO={{40}^{\circ }}\text{ }\!\!\{\!\!\text{ base }\angle s\text{ of isso }\vartriangle \} \\ & \angle POM=\angle OMN={{40}^{\circ }}\text{ }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\\end{align}$
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