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
10)
 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 $S = r\theta$.