Question

find the measure of the missing angles.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Angle \(b\) and the \(36^{\circ}\) angle are vertical angles.
So \(b = 36^{\circ}\)

Step2: Identify supplementary - angle relationship

Angle \(b\) and angle \(c\) are supplementary (they form a straight - line). The sum of supplementary angles is \(180^{\circ}\).
\(c=180^{\circ}-b\)
Substitute \(b = 36^{\circ}\) into the formula: \(c = 180 - 36=144^{\circ}\)

Answer:

\(b = 36\), \(c = 144\)