Question

find the measure of the missing angles

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle \(a\) and the \(120^{\circ}\) angle are vertical angles, so \(a = 120^{\circ}\).

Step2: Use linear - pair property

The sum of angles in a linear pair is \(180^{\circ}\). Angle \(a\) and angle \(c\) form a linear pair. So \(c=180 - a\). Substituting \(a = 120^{\circ}\), we get \(c = 180-120=60^{\circ}\). Also, angle \(c\) and angle \(b\) are vertical angles, so \(b = c=60^{\circ}\).

Answer:

\(b = 60\), \(c = 60\)