In the diagram $\angle PSR={{22}^{{}^\circ }},\text{ }\angle SPQ={{58}^{{}^\circ }}$ and Calculate the obtuse angle QRS
99o
100o
121o
165o
\[\begin{align} & \text{Produce line }QR\text{ to line }SP\text{ to meet at point }B \\ & \angle PBQ+\angle BPQ+\angle BQP={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ }\angle \text{s in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle PBQ+{{58}^{\circ }}+{{41}^{\circ }}={{180}^{\circ }} \\ & \angle PBQ={{81}^{\circ }} \\ & \angle SBR={{180}^{\circ }}-\angle PBQ={{180}^{\circ }}-{{81}^{\circ }}={{99}^{\circ }} \\ & \angle QRS=\angle SBR+\angle BSR\text{ } \\ & \text{ }\!\!\{\!\!\text{ sum of two opposite angle of a triangle }\!\!\}\!\!\text{ } \\ & \angle QRS={{99}^{\circ }}+{{22}^{\circ }}={{121}^{\circ }} \\\end{align}\]