Question

line y is parallel to line z. find the measures of the angles q, r, and s. m∠q = m∠r = m∠s = q 140° y z r s

Explanation:

Step1: Use vertical - angle property

$\angle Q$ and the $140^{\circ}$ angle are vertical angles. Vertical angles are equal. So $m\angle Q = 140^{\circ}$.

Step2: Use corresponding - angle property

Since line $y$ is parallel to line $z$, $\angle Q$ and $\angle S$ are corresponding angles. Corresponding angles are equal when two lines are parallel. So $m\angle S=140^{\circ}$.

Step3: Use linear - pair property

$\angle S$ and $\angle R$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle R = 180 - 140=40^{\circ}$.

Answer:

$m\angle Q = 140^{\circ}$
$m\angle R = 40^{\circ}$
$m\angle S = 140^{\circ}$