Adjacent Angles
Two angles are Adjacent if they have a common side and a common vertex (corner point) and don't overlap.
Angle ABC is adjacent to angle CBD Because:


What Is and Isn't an Adjacent Angle
These ARE Adjacent Angles they share a vertex and a side 
NOT Adjacent Angles they only share a vertex, not a side 
NOT Adjacent Angles they only share a side, not a vertex 
Don't Overlap!
ALSO the angles must not overlap.
NOT Adjacent Angles angles a and b overlap 