Answer
$\angle x=155^{\circ}$
$\angle y=155^{\circ}$
$\angle z=25^{\circ}$
Work Step by Step
In the picture, we can see that $\angle x$ and the other angle ($25^{\circ}$) form a straight angle, they are supplementary angles, so they add up to $180^{\circ}$.
$\angle x+25^{\circ}= 180^{\circ}$
$\angle x= 180^{\circ}-25^{\circ}$
$\angle x= 155^{\circ}$
The same is true with $\angle z$:
$\angle y= 155^{\circ}$
If we consider $\angle z$ and $\angle y$, they are also supplementary angles, so they add up to $180^{\circ}$
$\angle z+\angle y=180^{\circ}$
$\angle z+155^{\circ}=180^{\circ}$
$\angle z= 180^{\circ}-155^{\circ}$
$\angle z=25^{\circ}$