Angle and it’s measurement.


IF a line is rotated on one of it’s end point without changing the position of it’s another end point or it is rotated on one of it’s end point the the configuration formed by initial arm , terminal arm and vertex or common end point is known as Angle.

An angle always has following things:

An initial arm.

A terminal arm.  and

A vertex.

As shown in figure below:

Configuration of an Angle.

An angle is said to be positive if the initial arm is rotated anti-clockwise direction and vice versa.

If the vertex of any angle is at the origin of a rectangular co-ordinate system the it is said to be in the standard position.

Often , in problem related to angle we assume the angle to be in standard position.

Measurement of Angle:

An angle is measured in terms of the amount of rotation done by initial arm in an angle. To measure an angle we assume an angle as standard or a unit of angle and compare the unknown angle with it.

On the basis of the definition of standard angle there are many types of angle measurement system the most commonly used two are described below:

Sexagesimal System.

In this system. The unit of angle measurement is a degree.

If aright angle(one fourth of a complete rotation) Is divided into 90 equal parts then each part or angle is regarded as a degree of angle. For smaller angle measurement a degree is divided into 60 equal parts and each part or angle is regarded to be a minute of angle. For further smaller angle measurement a minute is further divided into 60 equal parts and each part or angle is regarded as a second of angle.

A degree is denoted by “°” , minute by “′” and a second by “″”

The angle of measurement in this system can be summarized as:

60″(60 seconds)=1′(1 minute)

60′(60 minute)=1°(1 degree)

90°(90 degree)=1 right angle.

Radian Measure:

In this system the unit of angle measurement is  a “radian”.

A radian is an angle subtended at the center of a circle by an arc equal in length to the radius of circle.

For example:

The angle θ is a radian if the arc AA′ is equal to the radius of circle in given figure:

A Radian Angle.

A radian is denoted by the symbol “c

Note: In any circle circumference = 2πr

so, 360°=2πc

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