What are vertical angles?

Vertical angles are defined as pairs of opposite angles formed when two lines intersect. When this intersection occurs, each pair of angles that are opposite each other is equal in measure. This property arises from the way angles are formed, indicating that when two lines cross, the angles that are not adjacent to each other (thus termed "vertical") have the same degree measure.

To illustrate, if two lines intersect and create four angles, the angles that are across from each other (for example, the top left and bottom right) are vertical angles. If one of those angles measures 50 degrees, the angle directly opposite will also measure 50 degrees, affirming that vertical angles are equal.

This characteristic of vertical angles is a fundamental principle in geometry, often utilized in various proofs and problems involving angle relationships. Understanding this concept is crucial as it lays the groundwork for more complex geometrical theorems and real-world applications, such as in architectural design or when solving problems involving parallel lines and transversals.