Adjacent angles share a side and a vertex. If angles only share a side but not a vertex, they are not adjacent. Adjacent angles can also be described as "next to" or "side-by-side" angles.
A word we use often in Geometry is this word Adjacent. You're going to use it in the beginning parts of Geometry and then once you get on Trigonometry as well. We'll hold of on adjacent sides for Trigonometry. But for now the key parts of an adjacent angle that they share a vertex, again the vertex is this point right here I'm going to draw a red dot. So this right here is a vertex. They have a side in common which sets them apart from vertical angles. So the side that these two angles share is that ray right there. So I could say that this angle one and two are adjacent because they share a vertex and they have a side in common. Now if you've been really technical, these two have to be coplanar which means that they're on the same plane.
So if I look at this triangle right here where I've drawn in a line segment we only have two adjacent angles. I'm going to write these as 3 and 4. These two angles right here I'll circle them, are not adjacent because they do not share vertex. So you can think of adjacent as kind of a word for next to.