waecmaths question:
In the diagram $\overline{ST}\parallel \overline{PQ}$, reflex angle SRQ =198o and $\angle RQP={{72}^{\circ }}$ . Find the value of y
Option A:
18o
Option B:
54o
Option C:
92o
Option D:
108o
waecmaths solution:
Draw a straight line AB parallel to ST and PQ passing through R$\begin{align} & \angle PQR=\angle QRB={{72}^{\circ }}\text{ }\!\!\{\!\!\text{ Alternate angle }\!\!\}\!\!\text{ } \\ & \angle SRB={{198}^{\circ }}-{{72}^{\circ }}={{126}^{\circ }} \\ & \angle ARS+\angle SRB={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ Sum of angles on a straight line }\!\!\}\!\!\text{ } \\ & \angle ARS={{180}^{\circ }}-{{126}^{\circ }}={{54}^{\circ }} \\ & y=\angle RST=\angle ARS={{54}^{\circ }}\text{ }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ } \\\end{align}$
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