waecmaths question:
In the diagram O is the centre of the circle $\overline{RT}$is a diameter, $\angle POT={{33}^{\circ }}$ and $\angle TOS={{76}^{\circ }}$. Use the diagram to answer question 19 and 20
19. Calculate the value of angle PTR
Option A:
73o
Option B:
67o
Option C:
57o
Option D:
37o
waecmaths solution:
$\begin{align} & \angle PRT=\angle PQT={{33}^{\circ }}\text{ }\!\!\{\!\!\text{ }\angle s\text{ in the same segment }\!\!\}\!\!\text{ } \\ & \angle RPT={{90}^{\circ }}\text{ }\!\!\{\!\!\text{ Angle in a semicircle }\!\!\}\!\!\text{ } \\ & \angle PTR+\angle PRT+\angle RPT={{180}^{\circ }} \\ & \angle PTR+{{33}^{\circ }}+{{90}^{\circ }}={{180}^{\circ }} \\ & \angle PTR={{180}^{\circ }}-{{123}^{\circ }}={{57}^{\circ }} \\\end{align}$
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