Question

what is the measure of ∠4? 100° 45° 50° 80°

Explanation:

Step1: Find the measure of ∠6

Since ∠6 and the \(100^{\circ}\) angle are adjacent angles on a straight line, we use the property that adjacent angles on a straight line sum to \(180^{\circ}\).
\(\angle6 = 180^{\circ}- 100^{\circ}=80^{\circ}\)

Step2: Use the property of parallel lines

Lines \(e\) and \(f\) are parallel. ∠4 and ∠6 are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal.
So, \(\angle4=\angle6\)

Answer:

\(80^{\circ}\)