In the intersection of lines, what must be true about the angle measures?

In the intersection of two lines, opposite angles, or vertical angles, are formed. These vertical angles are always equal to each other due to the nature of how lines intersect. When two lines cross, they create two pairs of vertical angles. Each angle in one pair is opposite the other, making them equal. Therefore, if angle A and angle C are vertical angles formed at the intersection, it is true that they are equal.

This principle is rooted in the properties of intersecting lines and provides a foundational understanding in geometry. Recognizing that vertical angles are congruent plays a significant role in solving problems related to angle relationships in various geometrical contexts. This understanding also reinforces the importance of angle relationships in constructing geometrical proofs or solving complex problems involving these angles.