Question

part 1 of 3
lines m and n are parallel. find the measures of angles x, y, and z in the figure.
m∠x = □°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle adjacent to the given $55^{\circ}$ angle and $\angle x$ are vertical angles. So $m\angle x = 55^{\circ}$.

Step2: Use corresponding - angle property

Since lines $m$ and $n$ are parallel, $\angle x$ and $\angle y$ are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So $m\angle y=55^{\circ}$.

Step3: Use linear - pair property

$\angle y$ and $\angle z$ form a linear - pair. A linear - pair of angles is supplementary, i.e., $m\angle y + m\angle z=180^{\circ}$. Substituting $m\angle y = 55^{\circ}$, we get $m\angle z=180 - 55=125^{\circ}$.

Answer:

$m\angle x = 55^{\circ}$, $m\angle y = 55^{\circ}$, $m\angle z = 125^{\circ}$