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 \(b\): The angles given (\(75^{\circ}\) and \(115^{\circ}\)) do not satisfy the conditions for alternate - exterior angles (alternate - exterior angles should be equal if lines are parallel) or same - side exterior angles (same - side exterior angles should be supplementary if lines are parallel, but \(75 + 115=190

eq180\)).

• For lines \(e\) and \(f\): The \(75^{\circ}\) angles are alternate - exterior angles. By the alternate - exterior angles converse (if two lines are cut by a transversal and the alternate - exterior angles are congruent, then the two lines are parallel), lines \(e\) and \(f\) are parallel.

Answer:

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