What are angles that are opposite each other when two lines intersect and are always congruent?

Vertical angles are formed when two lines intersect, creating pairs of angles that are opposite each other. By definition, vertical angles are always congruent, meaning they have the same measure. This congruence arises from the fact that when the intersecting lines create two pairs of angles, each pair of vertical angles shares a common vertex and is formed by the same two lines.

For example, if two lines intersect and create angles of 30 degrees and 150 degrees at one intersection, the angles opposite (the vertical angles) will also be 30 degrees and 150 degrees respectively, confirming that they are congruent. This property is key in various geometric proofs and problems.

The other types of angles mentioned have distinct characteristics: complementary angles are two angles that add up to 90 degrees, adjacent angles share a common arm and vertex but do not necessarily have to be congruent, and supplementary angles add up to 180 degrees. Thus, the unique property of vertical angles being always congruent sets them apart as the correct choice in this context.