Basic Terms and Angle Pairs

Core concept

For example, if two lines cross and one of the four resulting angles measures 65°, the angle directly opposite it (vertically opposite) also measures 65°, while the two angles adjacent to it (forming linear pairs with the 65° angle) each measure 180°-65°=115°. These fundamental angle relationships, proven through basic geometric reasoning, are used repeatedly throughout more advanced geometric proofs involving parallel lines, triangles, and polygons.