You can do a "show-and-tell" with this problem:

Draw a pair of adjacent angles on a sheet of
paper like this:



Those two adjacent angles are indeed coplanar.

But now let's fold the paper along their common side, like this:



and you can see the two angles are still adjacent,
however they are in two different planes.  Therefore
the answer is: 

Adjacent angles are not necessarily coplanar.

Edwin