Question

answer attempt 2 out of 2
$g=square^{circ}$ $h = square^{circ}$
$k=square^{circ}$ $m=square^{circ}$

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $g$ and the $119^{\circ}$ angle are vertical angles, so $g = 119^{\circ}$.

Step2: Use supplementary - angle property

Angles $h$ and the $119^{\circ}$ angle are supplementary (a linear - pair). Since the sum of angles in a linear - pair is $180^{\circ}$, then $h=180 - 119=61^{\circ}$.

Step3: Use vertical - angle property

Angle $k$ and the $121^{\circ}$ angle are vertical angles, so $k = 121^{\circ}$.

Step4: Use supplementary - angle property

Angles $m$ and the $121^{\circ}$ angle are supplementary (a linear - pair). Since the sum of angles in a linear - pair is $180^{\circ}$, then $m = 180-121 = 59^{\circ}$.

Answer:

$g = 119^{\circ}$
$h = 61^{\circ}$
$k = 121^{\circ}$
$m = 59^{\circ}$