waecmaths question:
The diagram shows a trapezium inscribed in a semi-circle. If O is the mid-point of WZ and $\left| WX \right|=\left| XY \right|=\left| YZ \right|$, calculate the value of m
Option A:
90o
Option B:
60o
Option C:
45o
Option D:
30o
waecmaths solution:
$\begin{align} & WO=OX=OY=OZ\text{ }\!\!\{\!\!\text{ radius of circle }\!\!\}\!\!\text{ } \\ & \text{At point O, } \\ & \angle WOX+\angle XOY+\angle YOZ=180{}^\circ \\ & \text{Note }\angle WOX=\angle XOY=\angle YOZ=60{}^\circ \\ & \text{Consider }\vartriangle OYZ \\ & OY=OZ\text{ }\!\!\{\!\!\text{ Radius of circle }\!\!\}\!\!\text{ } \\ & \angle OZY=\angle OYZ=m \\ & \angle OZY+\angle OYZ+\angle YOZ=180{}^\circ \\ & m+m+60{}^\circ =180{}^\circ \\ & 2m=120{}^\circ ,\text{ }m=60{}^\circ \\\end{align}$
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