Angles and angle pairs | Geometry

What an angle is

An angle with vertex $$B$$ and sides through $$A$$ and $$C$$ is written $\angle ABC$ (vertex in the middle), or $\angle B$ if there's no confusion. Its measure in degrees is written $m\angle ABC$ .

Classifying angles

Type	Measure
acute	between $$0°$$ and $$90°$$
right	exactly $$90°$$ (marked with a small square)
obtuse	between $$90°$$ and $$180°$$
straight	exactly $$180°$$ : the sides are opposite rays

The angle addition postulate

Special angle pairs

The complement of $$48°$$ is $$42°$$ ; its supplement is $$132°$$ .

Why? If $\angle 1$ and $\angle 2$ form a linear pair, and so do $\angle 2$ and $\angle 3$ , then $m\angle 1 = 180° - m\angle 2 = m\angle 3$ .

Angle bisectors

If $\overrightarrow{BD}$ bisects $\angle ABC$ and $m\angle ABC = 130°$ , then $m\angle ABD = m\angle DBC = 65°$ .

Practice

Quick check

What is the complement of a $$25°$$ angle?

Quick check

Two lines intersect. One angle measures $$130°$$ . What is the measure of the angle vertical to it?

Type	Measure
acute	between $\(0°\)$ and $\(90°\)$
right	exactly $\(90°\)$ (marked with a small square)
obtuse	between $\(90°\)$ and $\(180°\)$
straight	exactly $\(180°\)$ : the sides are opposite rays