Question

lines a and b are parallel. the m∠1 = 71°. what is the measurement of ∠5?

Explanation:

Step1: Find the measure of ∠3

Since ∠1 and ∠3 are same - side interior angles and lines \(a\) and \(b\) are parallel, \(\angle1+\angle3 = 180^{\circ}\). Given \(\angle1 = 71^{\circ}\), then \(\angle3=180^{\circ}-\angle1\).

$$ \angle3 = 180^{\circ}- 71^{\circ}=109^{\circ} $$

Step2: Find the measure of ∠5

\(\angle3\) and \(\angle5\) are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are equal. So \(\angle5=\angle3\).

Answer:

\(109^{\circ}\)