To show the work for the given statement, we can draw two parallel lines cut by a transversal and label all the possible angle measures. The alternate exterior angles will be congruent, not supplementary.
When two parallel lines are cut by a transversal, several pairs of angles are formed. The given statement "the alternate exterior angles are supplementary" is not accurate. The correct statement is that "the alternate exterior angles are congruent" when two parallel lines are cut by a transversal. The correct pairs of angles formed when parallel lines are cut by a transversal are:
Corresponding Angles: These are equal in measure.
Alternate Interior Angles: These are equal in measure.
Alternate Exterior Angles: These are equal in measure.
Consecutive Interior Angles: These are supplementary, meaning they add up to 180 degrees.