Question 46

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waecmaths question: 

In the diagram. Find the size of the angle marked ao

Option A: 

60o 

Option B: 

80o

Option C: 

120o

Option D: 

160o

waecmaths solution: 

$\begin{align}  & \angle RO{{T}_{reflex}}={{280}^{\circ }} \\ & \angle RO{{T}_{acute}}={{360}^{\circ }}-{{280}^{\circ }}={{80}^{\circ }}\text{   }\!\!\{\!\!\text{ sum of angles at a point }\!\!\}\!\!\text{ } \\ & \angle RST=\tfrac{1}{2}\angle RO{{T}_{reflex}}=\tfrac{1}{2}({{280}^{\circ }})={{140}^{\circ }}\text{   }\!\!\{\!\!\text{ }\angle \text{ at cirumference}=\tfrac{1}{2}\angle \text{ at centre }\!\!\}\!\!\text{ } \\ & a={{360}^{\circ }}-\angle RO{{T}_{acute}}-\angle ORS-\angle STO\text{   }\!\!\{\!\!\text{ sum of }\angle s\text{ in a quad }\!\!\}\!\!\text{ } \\ & a={{360}^{\circ }}-{{140}^{\circ }}-{{60}^{\circ }}-{{80}^{\circ }}={{80}^{\circ }} \\\end{align}$

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