What is the positive difference in the degree measures of alternate interior angles formed by a transversal of two parallel lines if they are complementary?

To understand the scenario presented, we need to recall the properties of parallel lines and a transversal. When two parallel lines are intersected by a transversal, they create several pairs of angles, including alternate interior angles. These angles are equal in degree measure.

The question states that these alternate interior angles are complementary to each other, which means that the sum of their measures is 90 degrees. Since alternate interior angles formed by the transversal of parallel lines are equal, if they are complementary, each must measure exactly 45 degrees (because 45 + 45 = 90).

Now, the positive difference between the measures of these two equal angles is computed as follows:

1. Measure of the first angle: 45 degrees

2. Measure of the second angle: 45 degrees

The positive difference is calculated by subtracting one measure from the other:

45 degrees - 45 degrees = 0 degrees.

Thus, the positive difference in degree measures of these alternate interior angles, when they are complementary, is indeed 0 degrees, validating the choice and confirming the understanding of the properties of angles formed by a transversal intersecting parallel lines.