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

## 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.

# 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.

## 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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