Question 20

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waecmaths question: 

Find the value of x in the diagram

Option A: 

281o

Option B: 

269o

Option C: 

201o

Option D: 

179o

waecmaths solution: 

$\begin{align}  & \angle AOB+\angle BOC+\angle OCD={{180}^{\circ }}\text{  }\!\!\{\!\!\text{ }\angle s\text{ on a st}\text{. line }\!\!\}\!\!\text{ } \\ & \text{4}{{\text{5}}^{\circ }}+\angle BOC+{{85}^{\circ }}={{180}^{\circ }} \\ & \angle BOC={{50}^{\circ }} \\ & \angle DOH=\angle AOB={{45}^{\circ }}\text{ }\!\!\{\!\!\text{ vertically opposite}\angle s\} \\ & \angle OHY=\angle DOH={{45}^{\circ }}\text{  }\!\!\{\!\!\text{ Alternate }\angle s\} \\ & \angle FHY=\angle EFH={{34}^{\circ }}\text{  }\!\!\{\!\!\text{ Alternate }\angle s\} \\ & \angle OHF=\angle FHY+\angle OHY={{34}^{\circ }}+{{45}^{\circ }} \\ & \angle OHF={{79}^{\circ }} \\ & x={{360}^{\circ }}-{{79}^{\circ }}={{281}^{\circ }}\text{  }\!\!\{\!\!\text{ }\angle s\text{ at a point }\!\!\}\!\!\text{ } \\\end{align}$

maths year: