Degree Measure

A central angle that is subtended by an arc equal in length to 1/360 of the circle's circumference, is said to have a measure of one degree, denoted $1^\circ.$ For a circle with circumference $C$ units, central angle of $\theta$ degrees subtended by an arc of $s$ units, this relationship can be expressed as the proportion

$$\frac{\theta^{\circ}}{360^{\circ}}=\frac{s}{C},$$

$\theta^{\circ}$ in decimal degrees; $s$ and $C$ in same units.

Thus if any two of $\theta, s,$ or $C$ are known, the third can be found with simple algebra.

A degree is often further divided into minutes (1/60 degree) and seconds (1/60 minute,) or as decimal degrees.

A $90^\circ$ angle is called a right angle. A $180^\circ$ angle is called a straight angle. Angles less than $90^\circ$ are said to be acute, while angles greater than $90^\circ$ but less than $180^\circ$ are said to be obtuse.