Question

find the measure of the missing angles.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle \(h\) and the \(127^{\circ}\) angle are vertical angles, so \(h = 127^{\circ}\).

Step2: Use linear - pair property

A linear pair of angles sums to \(180^{\circ}\). Since \(h + g=180^{\circ}\) and \(h = 127^{\circ}\), then \(g=180 - 127=53^{\circ}\).

Step3: Use vertical - angle property for other angles

Angle \(m\) and the \(98^{\circ}\) angle are vertical angles, so \(m = 98^{\circ}\).

Step4: Use linear - pair property for other angles

Since \(m + k=180^{\circ}\) and \(m = 98^{\circ}\), then \(k=180 - 98 = 82^{\circ}\).

Answer:

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