Adjacent angles and vertical angles always share a common vertex, so they’re literally joined at the hip. Complementary and supplementary angles can share a vertex, but they don’t have to. Here are the definitions for the different angle pairs:

**Adjacent angles:**Adjacent angles are neighboring angles that have the same vertex and that share a side; also, neither angle can be inside the other. This very simple idea is kind of a pain to define, so just check out the figure below — a picture’s worth a thousand words.None of the unnamed angles to the right are adjacent because they either don’t share a vertex or don’t share a side.

**Warning:**If you have adjacent angles, you can’t name any of the angles with a single letter.Instead, you have to refer to the angle in question with a number or with three letters.

**Complementary angles:**Two angles that add up to 90° (or a right angle) are complementary. They can be adjacent angles but don’t have to be.**Supplementary angles:**Two angles that add up to 180° (or a straight angle) are supplementary. They may or may not be adjacent angles.Such angle pairs are called a

*linear*pair.Angles

*A*and*Z*are supplementary because they add up to 180°.**Vertical angles:**When intersecting lines form an X, the angles on the opposite sides of the X are called vertical angles.Two vertical angles are always the same size as each other. By the way, as you can see in the figure, the

*vertical*in*vertical angles*has nothing to do with the up-and-down meaning of vertical.