Question 43

loading...

Prev/Next links

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$\begin{align}  & \angle PQR=\angle QRB={{72}^{\circ }}\text{    }\!\!\{\!\!\text{ Alternate angle }\!\!\}\!\!\text{ } \\ & \angle SRB={{198}^{\circ }}-{{72}^{\circ }}={{126}^{\circ }} \\ & \angle ARS+\angle SRB={{180}^{\circ }}\text{     }\!\!\{\!\!\text{ Sum of angles on a straight line }\!\!\}\!\!\text{ } \\ & \angle ARS={{180}^{\circ }}-{{126}^{\circ }}={{54}^{\circ }} \\ & y=\angle RST=\angle ARS={{54}^{\circ }}\text{      }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ } \\\end{align}$

maths year: