Angle Relationships

Basic Angle Types

Acute angle: $0° < \theta < 90°$

Right angle: $\theta = 90°$

Obtuse angle: $90° < \theta < 180°$

Straight angle: $\theta = 180°$

Complementary Angles

Two angles are complementary if their sum is $90°$.

Example: $35°$ and $55°$ are complementary because $35° + 55° = 90°$

Supplementary Angles

Two angles are supplementary if their sum is $180°$.

Example: $120°$ and $60°$ are supplementary because $120° + 60° = 180°$

Vertical Angles

When two lines intersect, vertical angles are opposite each other.

Key Property: Vertical angles are always congruent (equal).

Linear Pair

Two adjacent angles that form a straight line.

Property: Linear pairs are supplementary (sum to $180°$).

Angle Addition Postulate

If point $B$ is in the interior of $\angle AOC$, then: $m\angle AOB + m\angle BOC = m\angle AOC$