What is the classification of angles created when two lines intersect, where non-adjacent angles are equal?

When two lines intersect, they form pairs of angles where non-adjacent angles are equal. These angles are referred to as vertical angles. Vertical angles are always formed in such a way that they are opposite each other at the intersection, and one can prove their equality based on the properties of intersecting lines and the definition of vertical angles.

To understand why vertical angles are equal, consider that the angles share the same vertex and are created by the same two intersecting lines. The relationship between these angles can be visualized as forming two pairs of opposing angles, each equal to each other due to being the result of linear pair formations from the intersecting lines. This concept is fundamental in geometry and offers a basis for further exploration of angle relationships.

In contrast, adjacent angles are those that share a common side and vertex but are not opposite to each other, which does not apply in this scenario. Additionally, complementary angles are defined specifically as two angles that add up to 90 degrees, unrelated to their spatial arrangement. Lastly, scalene angles refer to triangles where all sides and angles are of different measures, which does not pertain to the angle relationships formed by intersecting lines. Thus, the classification of angles where non-adjacent angles are equal