Some of the angle pairs can be confusing to understand. To help you figure out what makes each one its own, you can go to the folowing website: http://www.mathsisfun.com/geometry/index.html
Scroll down until you see Angles. There you will find links to explanations of vertical, adjacent, complimentary, supplementary, and interoir/exterior angles along with many others like linear and congruent
My favorite angle pair is a linear pair because they're both adjacent and complimentary. I find it cool to think about how they're both formed into one angle. This means that they have a shared ray and add up to 180 degrees. A good way to remember this is to think of the word linear. It mean line right? So a line is an angle of 180 degrees. So as long as they add up to that and share a ray, or their angle sides are the same, you have a linear pair.