Question

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. Angle $x$ and the $47^{\circ}$ angle are vertical angles. So $x = 47^{\circ}$.

Step2: Use corresponding - angle property

Since lines $m$ and $n$ are parallel, angle $y$ and the $47^{\circ}$ angle are corresponding angles. So $y=47^{\circ}$.

Step3: Use linear - pair property

Angle $y$ and angle $z$ form a linear - pair. A linear - pair of angles is supplementary, i.e., $y + z=180^{\circ}$. Substitute $y = 47^{\circ}$ into the equation: $z=180^{\circ}-y=180 - 47=133^{\circ}$.

Answer:

$m\angle x = 47^{\circ}$, $m\angle y = 47^{\circ}$, $m\angle z = 133^{\circ}$