System of Measurement of Angles

Sexagesimal System

$1 \text{ right angle } = 90^{\circ}$

$1^{\circ} = 60 \text{ minutes } = 60'$

$1' = 60 \text{ seconds } = 60''$

Centesimal System

$1 \text{ right angle } = 100 \text{ grads } = 100^g$

$1 \text{ grade } = 100 \text{ minutes } = 100'$

$1 \text{ minute } = 100 \text{ seconds } = 100''$

Circular System

Radian: One radian $(1^c)$, is the measure of the angle subtended at the center of a circle by an arc of length equal to the radius of the circle.

$\displaystyle 1^c = \frac{angle}{\pi}$

The number of radians in an angle subtended by an arc of a circle is equal to $\frac{arc}{radius}$

$\displaystyle 1^c = \frac{180^o}{\pi}$