Sexagesimal System (Degree Measure)

Sexagesimal System (Degree Measure)

In the sexagesimal ("base-60") system, the unit of angle measurement is the degree. One complete rotation is divided into $360$ equal parts, and the measure of each part is called one degree, written $1°$:

Because a whole degree is often too coarse a unit, it is further subdivided using base $60$, exactly as an hour is subdivided into minutes and seconds:

• $\frac{1}{60}$ of a degree is called one minute, written $1'$, so $1° = 60'$.
• $\frac{1}{60}$ of a minute is called one second, written $1''$, so $1' = 60''$.

Using this unit, the special angles of the previous section have the familiar degree measures

$m\angle(\text{one rotation angle}) = 360°, \qquad m\angle(\text{straight angle}) = 180°, \qquad m\angle(\text{right angle}) = 90°$ …