$\begin{align}  & \angle WUS={{180}^{\circ }}-\angle VUW={{180}^{\circ }}-{{110}^{\circ }}={{70}^{\circ }} \\ & \text{ }\!\!\{\!\!\text{ sum of }\angle s\text{ on a straight line }\!\!\}\!\!\text{ } \\ & \angle SWU={{180}^{\circ }}-\angle WUS-\angle WSU\text{  }\!\!\{\!\!\text{ }\angle s\text{ in a }\vartriangle \} \\ & \angle SWU={{180}^{\circ }}-{{40}^{\circ }}-{{70}^{\circ }}={{70}^{\circ }} \\ & \angle XYW=\angle SWU-\angle YXW\text{ } \\ & \text{ }\!\!\{\!\!\text{ sum of two opp}\text{. }\angle s\text{ in }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & \angle XYW={{70}^{\circ }}-{{40}^{\circ }}={{30}^{\circ }} \\ & \angle XYW+\angle TYW={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ sum of }\angle s\text{ on a st}\text{. line }\!\!\}\!\!\text{ } \\ & \angle TYW={{180}^{\circ }}-{{30}^{\circ }}={{150}^{\circ }} \\\end{align}$