Are ∠1 and ∠2 adjacent angles?

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### Video Transcript

Are angles one and two adjacent angles?

In the diagram, we can see three lines. And the way that these lines have been drawn, we can also see three angles. To help us identify them, they’re labelled one, two, and three. Angle one is this angle here. Angle two is between these two lines here. And angle three is this larger angle that we can see here. Now, we don’t need to worry about angle three, because the question asks us simply about angles one and two. Are angles one and two adjacent angles?

Let’s remind ourselves what adjacent angles are. Adjacent angles have two things in common. Firstly, they share a common vertex. A vertex is simply the point from which all the rays that make up the angles come from. So they all come from one point. The second thing that adjacent angles have in common is that they share a common side. One of the rays or sides of the angle is shared by two angles if they’re adjacent. In this example, we can see that the blue line is a side that’s common between angle 𝑎, but also angle 𝑏.

Let’s use these two rules about adjacent angles to help us find out whether angles one and two in our diagram are adjacent. Firstly, do they share a common vertex? Well, if we begin by looking at angle one, we could mark the vertex by drawing an orange dot. The vertex for angle one is here. But if we look at angle two and mark the vertex here with a pink dot, we can see that the vertex for angle two is here. Both sides that make the angle come from this point. Angles one and two don’t share a common vertex. So they can’t be adjacent angles.

Let’s see now whether they share a common side. Well, you could say that they do. This part of the line from angle two is shared with angle one. But it’s not the whole of the line that’s used in angle one. And so we can’t really say that angles one and two share a common side. We’ve used the two rules for adjacent angles to prove that angles one and two are not adjacent angles. And so we can give a very simple answer to the question.

Are angles one and two adjacent angles? No.