Question

which lines are parallel? justify your answer. lines c and f are parallel because their same side exterior angles are congruent. lines c and f are parallel because their alternate exterior angles are congruent. 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.

Explanation:

• Lines \(c\) and \(f\):
• The same - side exterior angles for lines \(c\) and \(f\) are \(76^{\circ}\) and \(116^{\circ}\). Since \(76 + 116=192

eq180\), they are not supplementary. Also, same - side exterior angles congruence is not a valid parallel line criterion.

• The alternate exterior angles for lines \(c\) and \(f\): One angle is \(76^{\circ}\) (for line \(a\) and \(c\) intersection) and there is no alternate exterior angle relationship that would make \(c\) and \(f\) parallel based on the given angles (\(116^{\circ}\) is not an alternate exterior angle to \(76^{\circ}\) for \(c\) and \(f\)).
• Lines \(a\) and \(b\):
• The same - side exterior angles for \(a\) and \(b\) are not relevant as the angles given (\(76^{\circ}\) and \(116^{\circ}\)) are not for \(a\) and \(b\) relationship.
• For lines \(c\) and \(f\), consider the transversal \(a\). The angle of \(76^{\circ}\) above line \(c\) and the \(76^{\circ}\) below line \(f\) are alternate exterior angles. When two lines are cut by a transversal and alternate exterior angles are congruent, the two lines are parallel.

Answer:

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