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Measurement of Angles

What is an Angle?

When a ray beginning from its initial point OA rotates its endpoint and takes the final position OB. It is called angle AOB. It is written as ∠AOB. See in fig.

What is an Angle

Some important used terms in angles are:

  • OA Initial side: the original ray
  • OB Terminal side: the final position of the ray after rotation
  • O Vertex: point of rotation

The amount of rotation from the initial side OA to the terminal side OB is called the measure of the angle. In this blog, the degree, radian and grade measure are discussed as they are the most important used units

Positive and Negative angle

The angle called positive angle, if the direction of rotation is anticlockwise. On the other hand the negative angle, if the direction of rotation is clockwise. See in fig.

Positive and Negative angle

How to Measure an Angle?

There are commonly two systems for angle measurement are as given below:

(i)Measurement Of Angle – Degree Measure

Degree Measure

The angle traced by a moving line about a point from is initial position to the terminating position in making 1\360 of the complete revolution of a circle is said to have a measure of 1 degree written as 10 .

  • The one-sixtieth part of a degree, i.e,1 0\60, is called a minute, written as 1′ or 1 degree = 60 minutes denoted as 1° = 60′
  • The one -sixtieth part of a minute, i.e,1’\60,is called a second, written as 1” or 1 minute = 60 seconds denoted as 1′ = 60″
  • Also, we define 1 right angle=90 0.
  • An angle measuring 180 0 is called a straight angle.

The Measurement of  the angles given below:Measurement of Angles

(ii)Measurement Of Angle – Radian Measure

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

We denote 1 radian by 1 c.

Relation Between Radian and Degree

We know that a complete circle subtends at its center an angle whose measure is 2π radians as well as 3600.

∴ (2π)c = 360°.

Hence,πc =180°.

1 radian= π/1800

1 degree= π​/180

Degree 30° 45° 60° 90° 180° 270° 360°
Radian π/ π/ π/3 π/2 π 3π/2