**Angle in Math: **Two rays with a common starting point form an angle. One of the rays of angle is called t**he initial side** and the other is the** terminal side**. The angle is identified by showing the direction of rotation from the initial side to the terminal side.

An angle is said to be positive/negative if the rotation is anti-clockwise/clockwise. Angles are usually denoted by Greek letters such as [katex]\alpha[/katex] (alpha), [katex]\beta[/katex](beta),[katex]\gamma[/katex] (gamma), [katex]\theta[/katex] (theta) etc.

There are two commonly used measurements for angle (in math): **Degrees and Radians**. which are explained as below:

**Sexagesimal System:(Degree, Minute and Second)**

If the initial ray [katex]\overline{OA} [/katex] rotates in an anti-clockwise direction in such a way that it coincides with itself, the angle then formed is said to be of 360 degrees ([katex]360^\circ[/katex])

One rotation (anti-clockwise) = [katex]360^\circ[/katex]

[katex]\frac12[/katex]rotation (anti-clockwise) = 180° is called a straight angle

[katex]\frac14[/katex]rotation (anti-clockwise) = 90° is called a right angle

1 degree (1°) is divided into 60 minutes (60′) and 1 minute ( 1’) is divided into 60 seconds

(60′′). As this system of measurement of angle owes its origin to the English and because 90,

60 are multiples of 6 and 10, so it is known as the English system or the Sexagesimal system.

Thus

1 rotation (anti-clockwise) = 360°.

One degree (1°) = 60’

One minute (1′) = 60”

**Circular System (Radians)**

There is another system of angular measurement, called the Circular System. It is most useful for the study of higher mathematics. Especially in Calculus, angles are measured in radians.**Definition**: **Radian is the measure of the angle subtended at the center of the circle by an arc, whose length is equal to the radius of the circle.**

Consider a circle of radius r. Construct an angle ∠AOB at the center of the circle whose rays cut of an arc [katex]\overset\frown{AB}[/katex] on the circle whose length is equal to the radius [katex]r[/katex].

Thus m AOB ∠ = 1 radian