Vertical angles:
Vertical Angles are the angles opposite each other when two lines cross.
https://www.mathsisfun.com/geometry/vertical-angles.html
The link has a visual of vertical angles.
Adjacent Angles:
Adjacent angles are two angles that share a common vertex point and a common side. They basically sit right next to each other.
https://www.mathsisfun.com/geometry/adjacent-angles.html
The link has a visual of adjacent angles.
Complementary Angles:
Two angles whose measures add to 90º.
Basically, together they make a right angle.
Supplementary Angles:
Two angles whose measures add to 180º.
Basically, together they form a straight line.