Adjacent Angles
Two angles are Adjacent when 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