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Concept of Angle - Arms, Vertex, Interior and Exterior Region

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definition

Angle: An angle is made up of two rays starting from a common starting/initial point. An angle is represented by the symbol ∠.

Arms of Angle: The two rays forming the angle are called the arms or sides of the angle.

Vertex of the angle: The common initial point of two rays is the vertex of the angle.

notes

Angle:

  • An angle is made up of two rays starting from a common initial point. 
  • An angle is represented by the symbol ∠.
  • The two rays forming the angle are called the arms or sides of the angle.
  • The common initial point is the vertex of the angle.

               

  • Two rays `vec(OP)  "and"  vec(OQ)` make ∠POQ (or also called ∠QOP).

                             

  • ∠P is the mean of ∠APB, ∠CPB, and ∠APC. Note that in specifying the angle, the vertex is always written as the middle letter.
  • Each angle has a measure generated by the rotation about the vertex. The measure is determined by the rotation of the terminal side about the initial side. A counter-clockwise rotation generates a positive angle measure. A clockwise rotation generates a negative angle measure.

  • The units used to measure an angle are either in degrees or radians.

  • An angle leads to three divisions of a region: On the angle, the interior of the angle, and the exterior of the angle.               

                     

  • Name of the angle: ∠PQR. 
    Vertex of the angle: ∠Q.
    Arms of the angle: Arm PQ and Arm QR.
  • In the figure above, points X lie in the interior of ∠PQR. Point P, Q, R, and S lie on the angle ∠PQR and Z lie on the exterior of angle ∠PQR.

                 

  • The portion common to both shadings is called the interior of ∠ABC. (Note that the interior is not a restricted area; it extends indefinitely since the two sides extend indefinitely).

Example

Name the angles in the given figure.

Angles of given polygon: ∠BAD, ∠ADC, ∠DCB, ∠CBA

Example

In the given diagram, name the point (s)


a) In the interior of ∠DOE
(b) In the exterior of ∠EOF
(c) On ∠EOF

(a) Point A

(b) Point C, Point A, Point D

(c) Point B, Point E, Point O, Point F

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Shaalaa.com | Angles Part - 1

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Angles Part - 1 [00:17:08]
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