Question

lines m and n are parallel. find the measures of angles x, y, and z in the figure.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $x$ and the $50^{\circ}$ angle are vertical angles. So $x = 50^{\circ}$.

Step2: Use corresponding - angle property

Since lines $m$ and $n$ are parallel, angle $y$ and the $50^{\circ}$ angle are corresponding angles. So $y=50^{\circ}$.

Step3: Use linear - pair property

Angle $y$ and angle $z$ form a linear pair. A linear pair of angles sums to $180^{\circ}$. So $z = 180 - y$. Substituting $y = 50^{\circ}$, we get $z=180 - 50=130^{\circ}$.

Answer:

$x = 50^{\circ}$, $y = 50^{\circ}$, $z = 130^{\circ}$