Types of Angle Pairs
When angles work together in geometry, they create special relationships. Complementary angles add up to exactly 90° (a right angle), while supplementary angles add up to exactly 180° (a straight line).
There are three important angle pair relationships you need to know. Linear pairs are two angles next to each other that form a straight line - they're always supplementary. Adjacent angles share both a side and a vertex (corner point). Finally, vertical angles appear across from each other when two lines intersect - these angles are always equal to each other.
These angle relationships aren't just definitions - they're actually theorems that can be proven mathematically. Once proven, you can use these theorems as reasons in geometric proofs. Two key theorems are the Linear Pair Theorem (if two angles form a linear pair, then they equal 180°) and the Vertical Angles Theorem (vertical angles are congruent).
💡 When solving angle problems with variables, set up equations based on the relationships and solve for the unknown. For example, if vertical angles are ° and °, set them equal: 5x-2=4x+25, which gives x=27.
