Question

find the measure of the missing angles.

Explanation:

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

Vertical angles are equal. Since the angle vertical to \(h\) is \(112^{\circ}\), \(h = 112^{\circ}\).

Step2: Use linear - pair property for \(g\)

A linear pair of angles sums to \(180^{\circ}\). So \(g=180 - 112=68^{\circ}\).

Step3: Use vertical - angle property for \(k\)

Vertical angles are equal. Since the angle vertical to \(k\) is \(92^{\circ}\), \(k = 92^{\circ}\).

Step4: Use linear - pair property for \(m\)

A linear pair of angles sums to \(180^{\circ}\). So \(m = 180-92 = 88^{\circ}\).

Answer:

\(h = 112^{\circ}\), \(g = 68^{\circ}\), \(k = 92^{\circ}\), \(m = 88^{\circ}\)