I will take a shot at helping you. ;)
An example of two adjacent angles would be bisecting a 90 degree angle. Picture or draw a 90 degree angle. Then starting at the point of the angle(Vertex) draw a line outward dividing the angle into two angles. Now you have two adjacent angles. Adjacent meaning they are side by side.
If you were to bisect the 90 degree angle evenly, you would have two angles equal to 45 degrees. ;)
The easiest way to envision vertical angles would be to think of a pair of scissors. When you open up the scissors you form two sets of vertical angles.
The two finger holes form an angle that is equal to the angle of the two blades. These two angles are vertical angles.
Consequently on each side, the handle and blade would form an angle that can be paired with the other handle and blade making another set of vertical angles.
Another way to describe this would be the letter "X".
The top and bottom are vertical angles and the left and right side form vertical angles.
VERTICAL ANGLES WILL ALWAYS HAVE THE SAME NUMBER OF DEGREES
I hope this helps you :)