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.