# 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: **d****egrees **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 __ __