Angle Measurement: What is Angle? Positive and Negative Angles: Measurement of Angle (For CBSE, ICSE, IAS, NET, NRA 2022)

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Title: Angle Measurement

  • The concepts of equality, sums, and differences of angles are important and used throughout geometry, but the subject of trigonometry is based on the measurement of angles.
  • A ray is named after the endpoint and another point on the ray e. g.
Angle Measurement

What is Angle?

  • The angle that is formed between two rays with the same endpoint is measured in degrees.
  • That point is called the vertex.
Illustration 2 for Title_Angle_Measurement

It is written as ∡ CAB

Positive and Negative Angles

Positive and Negative Angle
  • An angle formed by a rotating ray is said to be positive or negative depending on whether its moves anticlockwise or clockwise direction respectively.
  • Positive angle: if the direction of rotation is anticlockwise
  • Negative angle: if the direction of rotation is clockwise

Measurement of Angle

  • A complete revolution, i.e.. when the initial and terminal sides are in the same position after rotating clockwise or anticlockwise, is divided into 360 units called degrees.
  • Therefore, if the rotation from the initial side to the terminal side is of a revolution, then the angle is said to have a measure of one degree.
  • It is denoted as

Examples

Illustration 3 for Measurement_of_Angle

Degree Measurement

Illustration 4 for Degree_Measurement
  • This is also called an English system.
  • Radian measure is slightly more complex than the degree measure. Imagine a circle with a radius of 1 unit.
  • After that imagine an arc of the circle having a length of 1 unit.
  • Angle subtended by this arc at the center of the circle has a measure of 1 radian.