If any two angles have a common side or vertex without overlapping each other, they are called adjacent angles. See the below image:
Angle XYZ and angle ZYD have a common side ZY and common vertex Y so the angle XYZ is adjacent to the angle ZYD
When is any angle not called adjacent angle?
As we know, there should be a common side and vertex for becoming adjacent angles. If these conditions are not fulfilled, then the angels will not be adjacent angles. See the below images:
1. When angles share only a vertex, they are not adjacent angles.
2. When angles share only a side, they are not adjacent angles.
3. When angles share the side and vertex, but they are overlapping each other.
Adjacent angles examples
Below images are the examples of adjacent angles: