Answer
$\angle x=100^{\circ}$
$\angle y=80^{\circ}$
$\angle z=80^{\circ}$
Work Step by Step
In the picture, we can see that $\angle y$ and the other angle ($100^{\circ}$) form a straight angle, they are supplementary angles, so they add up to $180^{\circ}$.
$\angle y+100^{\circ}= 180^{\circ}$
$\angle y= 180^{\circ}-100^{\circ}$
$\angle y= 80^{\circ}$
The same is true with $\angle z$:
$\angle z= 80^{\circ}$
If we consider $\angle x$ and $\angle y$, they are also supplementary angles, so they add up to $180^{\circ}$
$\angle x+\angle y=180^{\circ}$
$\angle x+80^{\circ}=180^{\circ}$
$\angle x= 180^{\circ}-80^{\circ}$
$\angle x=100^{\circ}$