Adjacent angles are angles that have a common vertex and a common side. So, in order to find pairs of adjacent angles, simply look for two angles that share a vertex and side. In this example, ∠FAE and ∠EAD both have vertex A and side AE, so they are adjacent. Another example is ∠BAC and ∠BAF. They both contain vertex A and side BA, so they are adjacent to one another.
To show you some examples of what do I mean by adjacent angles. We’re going to look to a problem here that’s asking you identify two pairs of adjacent angles. Well if I start by looking at one angle FAE, so I’m going to look at that angle right there, angle FAE. There are two possibilities for an adjacent angle, here’s our vertex and it has two different sides so we could use angle EAD. So I’m going to say that these two angles are adjacent.
I could also have used angle FAB. So let’s say FAE and EAD are adjacent angles. Let’s pick another angle, let’s say we used angle BAC, notice I used the same number of markings here because they have to be congruent. These are a vertical pair of angles. So BAC, so angle BAC and another adjacent angle could be this large obtuse angle BAF. So I’m going to write angle BAF. Adjacent angles share a common vertex and a common side.