Question 44

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waecmaths question: 

In the diagram, PX is a tangent to the circle and PST is an equilateral triangle. Calculate $\angle PTS$

Option A: 

60o

Option B: 

90o

Option C: 

120o 

Option D: 

150o

waecmaths solution: 

$\begin{align}  & \text{In a equilateral triangle, each angle is 6}{{\text{0}}^{\circ }} \\ & \angle TRS=\angle RST=\angle STR={{60}^{\circ }}\text{   }\!\!\{\!\!\text{ }\angle s\text{ in a equilateral }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle RTP=\angle RST={{60}^{\circ }}\text{   }\!\!\{\!\!\text{ }\angle s\text{ in a alternate segment }\!\!\}\!\!\text{ } \\ & \angle PTS=\angle RST+\angle RTP \\ & \angle PTS={{60}^{\circ }}+{{60}^{\circ }}={{120}^{\circ }} \\\end{align}$

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