Results of Angles with Degree and Radian

1) ANGLE: The union of two non colinear rays which have a common end point is called an angle.

2) RADIAN: An angle subtended at the center of a circle by an arc of length equal to the radius of the circle is called the angle of one radian.

3) A circle contains $= 2\pi$ radians

4) A circle contains $= {180^ \circ }$ degrees

5) $\pi$ radians $= 180$ degrees

6) $1$ degree $= 60$ minutes$= 60'$

7) $1$ minute $= 60$ seconds $= 60''$

8) $1$ radian $= \frac{{{{180}^ \circ }}}{\pi } = {57.295778^ \circ } = {57^ \circ }17'44.8''$

9) ${1^ \circ } = \frac{\pi }{{180}} = 0.01745$ radian

Degrees	${30^ \circ }$	${45^ \circ }$	${60^ \circ }$	${90^ \circ }$	${120^ \circ }$	${135^ \circ }$	${150^ \circ }$	${180^ \circ }$
Radians	$\frac{\pi }{6}$	$\frac{\pi }{4}$	$\frac{\pi }{3}$	$\frac{\pi }{2}$	$\frac{{2\pi }}{3}$	$\frac{{3\pi }}{4}$	$\frac{{5\pi }}{6}$	$\pi$

11) If $\theta$ is the angle (measured in radians) subtended at the center of a circle of radius $r$ by an arc of length $S$, then $S = r\theta$.