Question 16

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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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