Question

find the measure of the missing angles.

Explanation:

Step1: Use vertical - angle property for \(h\) and \(g\)

Vertical angles are equal. Since the angle adjacent to \(h\) is \(127^{\circ}\), and \(h\) and the \(127^{\circ}\) angle are vertical angles, \(h = 127^{\circ}\). Also, \(g\) and the \(127^{\circ}\) angle are supplementary (linear - pair). So \(g=180^{\circ}- 127^{\circ}=53^{\circ}\).

Step2: Use vertical - angle property for \(m\) and \(k\)

Since \(m\) and the \(98^{\circ}\) angle are vertical angles, \(m = 98^{\circ}\). And \(k\) and the \(98^{\circ}\) angle are supplementary (linear - pair), so \(k = 180^{\circ}-98^{\circ}=82^{\circ}\).

Answer:

\(h = 127^{\circ}\), \(g = 53^{\circ}\), \(m = 98^{\circ}\), \(k = 82^{\circ}\)