Question

which lines are parallel? justify your answer. lines a and b are parallel because their alternate exterior angles are congruent. lines a and b are parallel because their same side exterior angles are supplementary. lines e and f are parallel because their alternate exterior angles are congruent. lines e and f are parallel because their same side exterior angles are congruent.

Explanation:

Step1: Identify angle - types

The \(75^{\circ}\) and \(115^{\circ}\) angles are same - side exterior angles formed by lines \(e\) and \(f\) with a transversal. The sum of \(75^{\circ}+115^{\circ}=190^{\circ}
eq180^{\circ}\), so they are not supplementary. The \(75^{\circ}\) angles are alternate exterior angles formed by lines \(e\) and \(f\) with a transversal.

Step2: Apply parallel - line theorem

If two lines are cut by a transversal and the alternate exterior angles are congruent, then the two lines are parallel. Here, the \(75^{\circ}\) alternate exterior angles show that lines \(e\) and \(f\) are parallel.

Answer:

Lines \(e\) and \(f\) are parallel because their alternate exterior angles are congruent.