$\begin{align}  & \mathbf{Construction}:\text{ }Project\text{ }line\text{ }QP\text{ }to\text{ }point\text{ }B \\ & \angle STO=\angle OST\text{   }\!\!\{\!\!\text{ Base }\angle \text{s of Isosceles }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \text{Consider }\vartriangle OST \\ & \angle STO+\angle OST+\angle SOT=180{}^\circ \text{   }\!\!\{\!\!\text{ sum of }\angle \text{s in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \text{50}{}^\circ \text{+50}{}^\circ \text{+}\angle SOT=180{}^\circ  \\ & \angle SOT=80{}^\circ  \\ & \angle SOT+\angle TOP=180{}^\circ \text{  }\!\!\{\!\!\text{ Sum of }\angle \text{s on str}\text{. line }\!\!\}\!\!\text{ } \\ & \text{80}{}^\circ \text{+}\angle TOP=180{}^\circ  \\ & \angle TOP=100{}^\circ  \\ & \angle OPQ=\angle TOP=100{}^\circ \text{  }\!\!\{\!\!\text{ Alternate Angles }\!\!\}\!\!\text{ } \\\end{align}$