Measurement of Angles
The measure of an angle is the amount of rotations required to get to the terminal side from the initial side. A common measure of an angle is derived by placing its vertex at the center of a circle of some fixed radius.
There are two commonly used measurements for angles: degrees and radians
Sexagesimal System (Degree, Minute and Second):
If the initial ray rotates in an anti-clockwise direction in such a way that it coincides with itself, the angle then formed is said to be of
degrees (
).
One rotation (anti-clockwise) =
rotation (anti-clockwise) =
is called a straight angle
rotation (anti-clockwise) =
is called a right angle.

1 degree () is divided into
minutes (
) and 1 minute (
) is divided into
seconds (
). As this system of measurement of angles originates from English and because
,
and multiplies of
and
, it is known as the English System or Sexagesimal System.
Thus rotation (anti-clockwise) =
One degree () =
One minute () =
Conversion from to a decimal form and vice versa.
(i) =
(ii) =
Example:
Convert to decimal form.
Solution:
and
Example:
Convert to the
form
Solution:
and
Therefore,
Thus