Look at the orange and yellow angles at the bottom. They must be equal since they are vertex angles. Similarly the yellow angle at the top is equal to the other alternate exterior angle.
Since the two alternate exterior angles are equal (given) then the two yellow angles must also be equal because each yellow angle is equal to one of the alternate exterior angles.
The yellow angles are alternate interior angles. If two lines are cut by a transversal and the alternate interior angles are equal the two lines are parallel. (Euclid's 5th postulate.)