Question

find the measure of the missing angles.

Explanation:

Step1: Vertical - angle property

Vertical angles are equal. Since the un - labeled angle adjacent to \(h\) and the \(90^{\circ}\) angle are vertical angles, \(h = 90^{\circ}\).

Step2: Supplementary - angle property for \(g\)

\(g\) and \(h\) are supplementary angles (a straight - line is \(180^{\circ}\)). So \(g=180 - h\). Substituting \(h = 90^{\circ}\), we get \(g = 90^{\circ}\).

Step3: Supplementary - angle property for \(m\)

The angle adjacent to \(m\) and the \(125^{\circ}\) angle are vertical angles, so the angle adjacent to \(m\) is \(125^{\circ}\). Since \(m\) and this angle are supplementary (\(180^{\circ}\) for a straight - line), \(m=180 - 125=55^{\circ}\).

Step4: Vertical - angle property for \(k\)

\(k\) and the \(125^{\circ}\) angle are vertical angles. So \(k = 125^{\circ}\).

Answer:

\(g = 90\), \(h = 90\), \(k = 125\), \(m = 55\)