Question

answer

$g=square^{circ}$ $h=square^{circ}$
$k=square^{circ}$ $m=square^{circ}$

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle vertical to the $123^{\circ}$ angle is $g$. So $g = 123^{\circ}$.

Step2: Use linear - pair property

A linear - pair of angles sums to $180^{\circ}$. Since $g$ and $h$ form a linear pair, $h=180 - g$. Substituting $g = 123^{\circ}$, we get $h = 180-123=57^{\circ}$.

Step3: Use vertical - angle property again

The angle vertical to the $81^{\circ}$ angle is $m$. So $m = 81^{\circ}$.

Step4: Use linear - pair property again

Since $m$ and $k$ form a linear pair, $k = 180 - m$. Substituting $m = 81^{\circ}$, we get $k=180 - 81 = 99^{\circ}$.

Answer:

$g = 123^{\circ}$, $h = 57^{\circ}$, $k = 99^{\circ}$, $m = 81^{\circ}$