Question

line f is parallel to line g. find the measures of the angles h, i, and j.
m∠h =
m∠i =
m∠j =
150° f h i g j

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle H$ and the $150^{\circ}$ angle are vertical angles. So, $m\angle H=150^{\circ}$.

Step2: Use corresponding - angle property

Since line $f$ is parallel to line $g$, $\angle I$ and the $150^{\circ}$ angle are corresponding angles. Corresponding angles of parallel lines are equal. So, $m\angle I = 150^{\circ}$.

Step3: Use linear - pair property

$\angle I$ and $\angle J$ form a linear - pair. A linear - pair of angles is supplementary, i.e., $m\angle I+m\angle J = 180^{\circ}$. Since $m\angle I = 150^{\circ}$, then $m\angle J=180 - 150=30^{\circ}$.

Answer:

$m\angle H = 150^{\circ}$
$m\angle I = 150^{\circ}$
$m\angle J = 30^{\circ}$