Theory:

The figure formed by two rays that share a common endpoint is called the angle.
ray.PNG
 
The rays forming the angle are known as its arms or sides. The common endpoint is known as its vertex.
 
An angle is also associated with 3 parts:
  • Interior
  • Angle/boundary
  • Exterior
ass.PNG
 
1. Interior of the curve:
 
The inside / inner region of the curve is referred to as the interior of the angle. In the above figure, the green coloured area is the interior of the angle.
 
2Angle / Boundary of the curve:
 
Angle/boundary is referred to the arms of the angle. In the above figure, the red point is on the arm of the angle.
 
3. Exterior of the curve:
 
The outside / outer region of the curve referred to as the exterior of the curve. In the above figure, the blue point depicts the exterior of the figure.
Naming an angle
ABC.PNG
 
Name the angles in the following ways:
 
1. Write the letter of the vertex alone.
 
The name of the above angle is \(\angle B\).
 
2. Write three capital letters with a vertex in the middle.
 
The name of the above angle is \(\angle ABC\) or \(\angle CBA\).
 
3. Label the arc with a number or lowers case or Greek letter.
 
The name of the above angle is \(\angle 1\).