$\begin{align}  & S\overset{\wedge }{\mathop{R}}\,Q=X\overset{\wedge }{\mathop{S}}\,R={{30}^{\circ }}\text{     }\!\!\{\!\!\text{ Corresponding Angles }\!\!\}\!\!\text{ } \\ & P\overset{\wedge }{\mathop{Q}}\,S=A\overset{\wedge }{\mathop{Q}}\,Y={{50}^{\circ }}\{\text{Vertically opposite angles }\!\!\}\!\!\text{ } \\ & P\overset{\wedge }{\mathop{Q}}\,S=Q\overset{\wedge }{\mathop{S}}\,R\text{              }\{\text{Alternate angles}\} \\ & S\overset{\wedge }{\mathop{Q}}\,R+R\overset{\wedge }{\mathop{S}}\,Q+S\overset{\wedge }{\mathop{R}}\,O={{180}^{\circ }}\text{    }\!\!\{\!\!\text{ Sum of }\angle \text{s in a }\Delta \} \\ & S\overset{\wedge }{\mathop{Q}}\,R+{{50}^{\circ }}+{{30}^{\circ }}={{180}^{\circ }} \\ & S\overset{\wedge }{\mathop{Q}}\,R={{180}^{\circ }}-({{50}^{\circ }}+{{30}^{\circ }})={{100}^{\circ }} \\\end{align}$