waecmaths question:
In the diagram PQ and PS are tangents to the circ centre O. If $\angle PSQ=m$, $\angle SPQ=n$ and $\angle SQR={{33}^{\circ }}$.
Find the value of (m + n)
Option A:
103o
Option B:
123o
Option C:
133o
Option D:
143o
waecmaths solution:
$\begin{align} & \angle LQR={{90}^{\circ }}\text{ }\!\!\{\!\!\text{ Tangent to a circle }\!\!\}\!\!\text{ } \\ & \angle PQS={{90}^{\circ }}-{{33}^{\circ }}={{57}^{\circ }} \\ & \text{Consider }\vartriangle PSQ \\ & m+n+{{57}^{\circ }}={{180}^{\circ }} \\ & m+n={{123}^{\circ }} \\\end{align}$
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