Adjacent Angle Pairs

Definition of adjacent angle pairs
If two angles have the same vertex and share a common side and have no interior points in common, then the two angles are adjacent.
Example 1:
adjacent angle pairs example1
In the figure above, angle 1 is the angle AOB and angle 2 is the angle AOC.
Note:
angle 1 and angle 2 have the same vertex that is the point O, same common side OA and have no interior points in common, therefore, angle 1 and angle 2 are an adjacent angle pair.
Example 2:
adjacent angle pairs example2
In the figure above, the vertex of the angle 1 is point A and the vertex of angle 2 is point E. Both of angle 1 and angle 2 have two different points. Therefore angle 1 and angle 2 are not an adjacent angle pair.
Example 3:
adjacent angle pair example3
In the figure above, angle 1 is the angle AOB and angle 2 is the angle COB. Both of angle 1 and angle 2 have the same vertex that is point O and the same common side OB, but they have interior points in common, that is, angle 2 is including angle 1. All points lie inside angle 1 are also lie inside angle 2. Therefore, angle 1 and angle 2 are not an adjacent angle pair.