### 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.