waecmaths question:
The diagram is a circle with centre O. PRST are points on the circle. Find the value of $\angle PRS$
Option A:
144o
Option B:
72o
Option C:
40o
Option D:
36o
waecmaths solution:
$\begin{align} & \angle PRS=\tfrac{1}{2}(8x)\text{ }\!\!\{\!\!\text{ }\angle \text{ at circum =}\tfrac{1}{2}\angle \text{ at centre }\!\!\}\!\!\text{ } \\ & \angle PRS=4x \\ & \angle PRS+\angle PTS={{180}^{\circ }}\{\text{sum of opposite }\angle \text{s in a cyclic quad }\!\!\}\!\!\text{ } \\ & 4x+x={{180}^{\circ }} \\ & x={{36}^{\circ }} \\ & \angle PRS=4\times {{36}^{\circ }}={{144}^{\circ }} \\\end{align}$
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