Question

answer attempt 1 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. Since the angle adjacent to \(h\) is \(109^{\circ}\), then \(h = 109^{\circ}\) because vertical angles are congruent. Also, \(g\) and the \(109^{\circ}\) angle are supplementary (a linear - pair). So \(g=180 - 109=71^{\circ}\).

Step2: Use vertical - angle property for the lower part

The angle adjacent to \(m\) is \(84^{\circ}\). Since vertical angles are equal, \(m = 84^{\circ}\). And \(k\) and the \(84^{\circ}\) angle are supplementary (a linear - pair), so \(k = 180-84 = 96^{\circ}\).

Answer:

\(g = 71^{\circ}\)
\(h = 109^{\circ}\)
\(k = 96^{\circ}\)
\(m = 84^{\circ}\)