Degree Measure

A degree, denoted $1^\circ$, comes from splitting one complete rotation ($360^\circ$ total) into $360$ equal parts, so $1^\circ$ is exactly $\dfrac{1}{360}$ of a full rotation. For finer measurement, a degree is further divided: $1' = \dfrac{1}{60}$ of a degree, and $1'' = \dfrac{1}{60}$ of a minute $= \dfrac{1}{3600}$ of a degree (mirroring how an hour splits into minutes and a minute into seconds when measuring time).

Classifying pairs of angles. Four useful relationships between two angles:

• Congruent angles: the two angles have exactly the same measure.
• Complementary angles: the two measures add up to $90^\circ$.
• Supplementary angles: the two measures add up to $180^\circ$.
• Conjugate angles: two angles between $0^\circ$ and $360^\circ$ whose measures add up to $360^\circ$. …