Question

lines m and n are parallel. find the measures of angles x, y, and z in the figure.
m∠x = (square^{circ})
m∠y = (square^{circ})
m∠z = (square^{circ})

Explanation:

Step1: Identify corresponding angles

Corresponding angles are equal when lines are parallel. Angle $x$ and the given $36^{\circ}$ angle are corresponding angles. So $x = 36^{\circ}$.

Step2: Identify vertical - angles

Angle $y$ and the given $36^{\circ}$ angle are vertical - angles. Vertical angles are equal. So $y=36^{\circ}$.

Step3: Identify supplementary angles

Angle $y$ and angle $z$ are supplementary (linear - pair). Since $y + z=180^{\circ}$ and $y = 36^{\circ}$, then $z=180 - 36=144^{\circ}$.

Answer:

$m\angle x = 36^{\circ}$
$m\angle y = 36^{\circ}$
$m\angle z = 144^{\circ}$