Question 24

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waecmaths question: 

In the diagram, O is the centre of the circle and $\angle PQR={{106}^{\circ }}$ .Find the value of y

Option A: 

16

Option B: 

37

Option C: 

74

Option D: 

127

waecmaths solution: 

$\begin{align}  & \angle PO{{R}_{reflex}}=2\times \angle PQR\text{  }\!\!\{\!\!\text{ }\angle \text{ at centre}=2\times \angle at\text{ cirumference }\!\!\}\!\!\text{ } \\ & \angle PO{{R}_{reflex}}=2\times {{106}^{\circ }}={{212}^{\circ }} \\ & \angle PO{{R}_{reflex}}+\angle PO{{R}_{acute}}={{360}^{\circ }}\text{   }\!\!\{\!\!\text{ }\angle s\text{ at a point }\!\!\}\!\!\text{ } \\ & {{212}^{\circ }}+2y={{360}^{\circ }} \\ & 2y={{148}^{\circ }} \\ & y={{74}^{\circ }} \\\end{align}$

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