Angle relationships refer to the connections between different angles formed when lines intersect or when shapes are created. Common types of angle relationships include complementary angles, which add up to 90 degrees, and supplementary angles, which total 180 degrees. Additionally, vertical angles are formed when two lines cross, creating pairs of opposite angles that are always equal. Understanding angle relationships is essential in geometry, as they help in solving problems related to triangles, polygons, and other geometric figures. These relationships also play a crucial role in real-world applications, such as architecture and engineering, where precise measurements are necessary for design and construction.