To determine the measure of alternate exterior angles formed by parallel lines, we utilize the principle that these angles are equal.

When a transversal intersects two parallel lines, it creates several pairs of angles. Among these are the alternate exterior angles, which are positioned on opposite sides of the transversal and outside the parallel lines. According to the properties of parallel lines, alternate exterior angles are always congruent. This means that if you know the measure of one alternate exterior angle, you can immediately ascertain the measure of its corresponding angle.

For instance, consider two parallel lines, denoted as $l_1$ and $l_2$, intersected by a transversal $t$. The points where $t$ intersects $l_1$ and $l_2$ can be labeled as points $A$ and $B$, respectively. If the angle formed at point $A$ on the left side of the transversal measures $120^\circ$, then the corresponding angle at point $B$ on the right side, which is also an alternate exterior angle, will likewise measure $120^\circ$.

In summary, the essential property to remember is that alternate exterior angles are congruent (equal in measure) when the lines are parallel. This property is particularly useful for solving various geometric problems, as it enables you to quickly and accurately determine unknown angle measures.