Are angle one and angle two
In this question, we are given a
figure containing three angles. And we are asked to determine if
two of the angles on the figure are adjacent.
We can start by recalling that an
angle is the combination of two rays that start at the same point called the vertex
of the angle and the rotation required to rotate the rays about the vertex so that
the sides of the angle are coincident. We can use this to mark angles one
and two on the diagram and the vertices of each angle, where we note that since the
size of the angles are not specified, we mean the angles with smaller measure.
To determine if the two angles are
adjacent, we can recall that we say that two angles are adjacent if they satisfy
three criteria. First, we need both angles to share
the same vertex. Second, we need both angles to
share a single common side. Third, we need the distinct sides
of the angle to lie on opposite sides of the side common to both angles.
We have already shown that the two
angles do not share the same vertex, so they cannot be adjacent. Hence, the answer is no, angles one
and two are not adjacent angles, since they have distinct vertices.
Although this is enough to answer
the question, it can be useful to see how to use these criteria to verify that two
angles are adjacent. To do this, let’s mark angle three
on the diagram and verify that it is adjacent to angle two. We can first note that both angles
share a vertex. Remember, this is the initial point
of the two rays that make up the sides of the angle. Next, we can see that the two
angles share a common side that we have highlighted.
Finally, we want to check that the
distinct sides of the angle lie on opposite sides of the common side. This is really just a check to make
sure that the angles are not overlapping. Instead, we want them to be
adjacent as shown. This confirms that angle two is
adjacent to angle three. However, the answer to this
question is no, angle one and angle two are not adjacent angles.