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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