Question

find the measure of the missing angles.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle \(h\) and the \(50^{\circ}\) angle are vertical angles, so \(h = 50^{\circ}\). Angle \(m\) and the \(39^{\circ}\) angle are vertical angles, so \(m=39^{\circ}\).

Step2: Use linear - pair property

A linear pair of angles sums to \(180^{\circ}\). For the linear - pair with \(h\) and \(g\), we have \(h + g=180^{\circ}\). Since \(h = 50^{\circ}\), then \(g=180^{\circ}-50^{\circ}=130^{\circ}\). For the linear - pair with \(m\) and \(k\), we have \(m + k=180^{\circ}\). Since \(m = 39^{\circ}\), then \(k=180^{\circ}-39^{\circ}=141^{\circ}\).

Answer:

\(h = 50^{\circ}\), \(g = 130^{\circ}\), \(m = 39^{\circ}\), \(k = 141^{\circ}\)