Question

1. find the measure of this angle.

Explanation:

Step1: Identify the relationship between angles

Angles on a straight line sum to \(180^{\circ}\). Angle \(1\) and the \(72^{\circ}\) angle are supplementary.

Step2: Calculate angle \(1\)

\(\angle1 = 180^{\circ}- 72^{\circ}\)
\(\angle1 = 108^{\circ}\)

Step3: Use the property of parallel lines and transversal (corresponding angles)

Since the two horizontal lines are parallel and cut by a transversal, \(\angle5\) and \(\angle1\) are corresponding angles. Corresponding angles are equal.

Answer:

\(108^{\circ}\)