1.4 Angles and Angle Measure

Notes

An angle is two rays with a common endpoint, the vertex. $\angle ABC$ has vertex $B$ (the middle letter).

• Measure in degrees: $m\angle ABC = 40^\circ$.
• Acute: less than $90^\circ$. Right: exactly $90^\circ$. Obtuse: between $90^\circ$ and $180^\circ$. Straight: exactly $180^\circ$.
• Angle Addition Postulate: if $D$ is in the interior of $\angle ABC$, then $m\angle ABD + m\angle DBC = m\angle ABC$.
• An angle bisector splits an angle into two congruent angles.
• Example: $\overrightarrow{BD}$ bisects $\angle ABC$ and $m\angle ABC = 70^\circ$, so $m\angle ABD = 35^\circ$.