How do you find the measure of alternate exterior angles in parallel lines?

To find the measure of alternate exterior angles in parallel lines, use the fact that they are equal.

When two parallel lines are cut by a transversal, several pairs of angles are formed. Among these are alternate exterior angles, which lie on opposite sides of the transversal and outside the parallel lines. According to the properties of parallel lines, alternate exterior angles are always equal. This means if you know the measure of one alternate exterior angle, you automatically know the measure of its corresponding angle.

For example, if you have two parallel lines, \( l_1 \) and \( l_2 \), and a transversal \( t \) cutting across them, you will see angles formed at the points where \( t \) intersects \( l_1 \) and \( l_2 \). Let's label these points of intersection as \( A \) and \( B \) respectively. If the angle at \( A \) on the left side of the transversal is \( 120^\circ \), then the angle at \( B \) on the right side of the transversal, which is an alternate exterior angle, will also be \( 120^\circ \).

To summarise, the key property to remember is that alternate exterior angles are congruent (equal in measure) when the lines are parallel. This property can be very useful in solving various geometric problems, as it allows you to determine unknown angle measures quickly and accurately.