Question 23

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waecmaths question: 

In the diagram O is the centre of the circle, $\angle MON={{80}^{\circ }}$ $\angle LMO={{10}^{\circ }}$ and $\angle LNO={{15}^{{}^\circ }}$.Calculate the value of x

Option A: 

40o

Option B: 

50o

Option C: 

55o

Option D: 

75o

waecmaths solution: 

$\begin{align}  & \text{Join point M and N together} \\ & \left| MO \right|=\left| NO \right|\text{    }\!\!\{\!\!\text{ Radius of a circle }\!\!\}\!\!\text{ } \\ & \angle OMN=\angle ONM\text{   }\!\!\{\!\!\text{ Base }\angle \text{s of Isso }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle MON+\angle OMN\angle ONM={{180}^{\circ }}\text{     }\!\!\{\!\!\text{ Sum of }\angle s\text{ in }\vartriangle \} \\ & {{80}^{\circ }}+y+y={{180}^{\circ }} \\ & 2y={{100}^{\circ }} \\ & y={{50}^{\circ }} \\ & \text{Considering }\vartriangle LMN \\ & \angle LMN+\angle MNL+\angle LMN={{180}^{{}^\circ }} \\ & {{60}^{\circ }}+{{65}^{\circ }}+x={{180}^{\circ }} \\ & x={{55}^{\circ }} \\\end{align}$ 

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