Vertical angles are the angles that are opposite each other when two lines intersect. When two lines cross, they form two pairs of vertical angles. Each pair consists of angles that are equal in measure. For example, if one angle measures 50 degrees, the angle directly across from it will also measure 50 degrees. These angles are important in geometry because they help establish relationships between different angles formed by intersecting lines. Understanding vertical angles can aid in solving various geometric problems and proofs, making them a fundamental concept in the study of geometry.