Angles & Angle Pairs

Complementary, supplementary, vertical, and adjacent angles.

The idea

Two angles are complementary when their measures add to $90°$, and supplementary when they add to $180°$. The complement of an angle is what remains of $90°$, and its supplement is what remains of $180°$, so finding either one is a subtraction.

Two angles are adjacent when they share a vertex and a side but do not overlap. Adjacent angles whose outer sides form a straight line are a linear pair, and a linear pair is always supplementary, because the two angles together fill a straight angle of $180°$.

Two lines crossing at a point $O$ make four angles, and the two opposite each other, sharing only the vertex, are vertical angles. Vertical angles are always equal: number the four angles $1, 2, 3, 4$ in order around the crossing, and the opposite angles $\angle 1$ and $\angle 3$ each form a linear pair with $\angle 2$, so each measures $180° - m\angle 2$.

Ways to work on it

• Walkthrough. The four angle-pair relationships with concrete measures.
• Practice. Find a complement or supplement.
• Hardest. Solve for x in a linear pair or vertical-angle equation.

Not sure where to start? Take the ten-question placement test.