Question

find the measure of the missing angles.

Explanation:

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

Vertical angles are equal. The angle vertical to the \(118^{\circ}\) angle is \(h\), so \(h = 118^{\circ}\). Also, \(g\) and the \(118^{\circ}\) angle are supplementary (a linear - pair), so \(g=180^{\circ}- 118^{\circ}=62^{\circ}\).

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

The angle vertical to the \(133^{\circ}\) angle is \(m\), so \(m = 133^{\circ}\). And \(k\) and the \(133^{\circ}\) angle are supplementary (a linear - pair), so \(k = 180^{\circ}-133^{\circ}=47^{\circ}\)

Answer:

\(h = 118^{\circ}\), \(g = 62^{\circ}\), \(m = 133^{\circ}\), \(k = 47^{\circ}\)