Vertical angles are angles that are the same (for example >< since they're the same). Adjacent angles are angles that share a side with another angles, such as \|, since they are sharing on angle that connects the two.
Now that you know what each is, you can tell that they are similar because they both have something in common. When dealing with vertical angles, you can tell that they are the same thing, meaning they each share the whole shape of the angle. Adjacent angles share one whole line together; therefore, showing you that both have a line in common.
adjacent angle A they both share angle A.
|
|
B____|________C
vertical angle they both share the same shape; they have four lines, and they also share angle C
a b
\ /
\ /
\ /
C \/
/\
/ \
/ \
/D \E
hope this helps :)