Question

find the measure of the missing angles.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $h$ and the $50^{\circ}$ angle are vertical angles, so $h = 50^{\circ}$. Angle $g$ and the $50^{\circ}$ angle form a linear - pair (sum to $180^{\circ}$). So $g=180 - 50=130^{\circ}$.

Step2: Use vertical - angle property for other angles

Angle $m$ and the $39^{\circ}$ angle are vertical angles, so $m = 39^{\circ}$. Angle $k$ and the $39^{\circ}$ angle form a linear - pair. So $k = 180-39 = 141^{\circ}$.

Answer:

$h = 50^{\circ}$, $g = 130^{\circ}$, $m = 39^{\circ}$, $k = 141^{\circ}$