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:

• For lines \(a\) and \(b\): Alternate exterior angles are not congruent (\(75^{\circ}

eq115^{\circ}\)), same - side exterior angles are \(75 + 115=190
eq180\) (not supplementary).

• For lines \(e\) and \(f\):
• Alternate exterior angles: The angle of \(75^{\circ}\) (for line \(a\) and \(e\)/\(f\)) and the corresponding angle (due to the property of parallel lines cut by a transversal) shows that the alternate exterior angles are congruent.
• Same - side exterior angles: Congruent same - side exterior angles (\(75^{\circ}\) and \(75^{\circ}\)) is not a condition for parallel lines (the condition for same - side exterior angles for parallel lines is that they are supplementary, i.e., sum to \(180^{\circ}\)).

Answer:

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