Question 50

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waecmaths question: 

In the diagram $\overline{OX}$ bisects $\angle YXZ$ and $\overline{OZ}$bisects $\angle YZX$If $\angle XYZ={{68}^{\circ }}$, Calculate the value of $\angle XOZ$

Option A: 

68o

Option B: 

72o

Option C: 

112o

Option D: 

124o

waecmaths solution: 

$\begin{align}  & \text{Sum of }\angle s\text{ is 18}{{\text{0}}^{\circ }} \\ & \angle XYZ+\angle XZY+\angle YXZ={{180}^{\circ }} \\ & {{68}^{\circ }}+\angle XZY+\angle YXZ={{180}^{\circ }} \\ & \angle XZY+\angle YXZ={{112}^{\circ }} \\ & \text{Since }\overline{OX}\text{ and }\overline{OZ}\text{ are bisectors of }\angle YXZ\text{ and }\angle YZX \\ & \angle OXZ+\angle OZX=\tfrac{1}{2}[\angle XZY+\angle YXZ] \\ & \vartriangle XOZ \\ & \tfrac{1}{2}[\angle XZY+\angle YXZ]+\angle XOZ={{180}^{\circ }} \\ & \tfrac{1}{2}[{{112}^{\circ }}]+\angle XOZ={{180}^{\circ }} \\ & {{56}^{\circ }}+\angle XOZ={{180}^{\circ }} \\ & \angle XOZ={{180}^{\circ }}-{{56}^{\circ }}={{124}^{\circ }} \\\end{align}$

maths year: