$\begin{align}  & \angle TXY=\angle XTY={{47}^{\circ }}\text{   (Base }\angle \text{s of issocele }\vartriangle \text{)} \\ & \angle XZT=\angle STZ={{34}^{\circ }}\text{    (Alternate angles)} \\ & \angle TXY+\angle XZT+\angle XTZ={{180}^{\circ }}\text{  (Sum of angles in a }\vartriangle \text{)} \\ & {{47}^{\circ }}+{{34}^{\circ }}+\angle XTZ={{180}^{\circ }} \\ & \angle XTZ={{180}^{\circ }}-({{47}^{\circ }}+{{34}^{\circ }})={{99}^{\circ }} \\ & \therefore \angle XTY+\angle YTZ={{99}^{\circ }} \\ & \angle YTZ={{99}^{\circ }} \\ & \angle YTZ={{99}^{\circ }}-{{47}^{\circ }}={{52}^{\circ }}\text{ } \\\end{align}$