Alternate interior angles are not necessarily complementary. In fact, they are equal when the two lines cut by a transversal are parallel.
To understand this, let’s define alternate interior angles. These are the pairs of angles that lie on opposite sides of the transversal and inside the two lines. For example, if line A and line B are parallel and line C is the transversal, then the alternate interior angles formed are equal in measure.
When the lines are parallel, the alternate interior angle theorem states that these angles are congruent, meaning they have the same degree measurement. Therefore, if one angle measures, say, 70 degrees, the alternate interior angle will also measure 70 degrees. Consequently, they cannot be complementary because complementary angles are two angles whose measures add up to 90 degrees.
However, if the lines are not parallel, alternate interior angles can indeed be different and may or may not form a complementary relationship. In summary, while alternate interior angles are congruent and equal when the lines are parallel, they are not necessarily complementary angles.