Question

1. given the two parallel lines cut by a transversal, what is the measure of ∠4 if m∠8 = 76°?

Explanation:

Step1: Find the measure of \(\angle 2\)

\(\angle 2\) and \(\angle 8\) are vertical angles. Vertical angles are equal. So \(m\angle 2=m\angle 8 = 76^{\circ}\)

Step2: Find the measure of \(\angle 4\)

\(\angle 2\) and \(\angle 4\) are same - side interior angles. For parallel lines cut by a transversal, same - side interior angles are supplementary (\(m\angle 2+m\angle 4 = 180^{\circ}\)).
Substitute \(m\angle 2 = 76^{\circ}\) into the equation: \(m\angle 4=180^{\circ}-m\angle 2\)
\(m\angle 4=180^{\circ}- 76^{\circ}=104^{\circ}\)

Answer:

\(104^{\circ}\)