waecmaths question:
In the diagram XY is a straight line, $\angle POX=\angle POQ$ and $\angle ROY=\angle QOR$ . Find the value of $\angle POQ+\angle ROY$
Option A:
60o
Option B:
90o
Option C:
100o
Option D:
120o
waecmaths solution:
$\begin{align} & \angle POX=\angle POQ=x \\ & \angle ROY=\angle QOY=y \\ & \therefore \angle POX+\angle POQ+\angle ROY+\angle QOY={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ sum of }\angle \text{s on a straight line }\!\!\}\!\!\text{ } \\ & x+x+y+y={{180}^{\circ }} \\ & 2x+2y={{180}^{\circ }} \\ & x+y={{90}^{\circ }} \\ & \angle POQ+\angle ROY={{90}^{\circ }} \\\end{align}$
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