Classify the following pair of
angles as complementary, supplementary, vertical, or neither.
In this question, we are given a
figure containing two angles, 1 and 2. We are asked to classify this pair
of angles as one of three types of angles, complementary, supplementary, or
vertical, or determine that this pair of angles cannot be classified as any of those
types of angles.
To answer this question, let’s
start by marking angles 1 and 2 on the given figure. We can see that these two angles
are adjacent angles since they share a common vertex and side and they are next to
each other. We can also note that angles 1 and
2 combine to make a right angle. We can recall that the sum of the
measures of adjacent angles is equal to the measure of the angle between the
distinct side of the two angles. So, we must have that the measure
of angle 1 plus the measure of angle 2 is 90 degrees, since they combine to make a
We can then recall that we say that
two angles are complementary if their measures sum to give 90 degrees. Hence, we can say that the pair of
angles given in the figure are complementary.
For due diligence, we can also
check if the angles can be classified as the other three options. First, we recall that we call two
angles supplementary angles if their measures sum to 180 degrees. That is, they can be made to form a
straight angle. We know that this is not true of
the angles given, since we have already shown that the sum of their measures is 90
Second, we recall that vertical, or
vertically opposite, angles are the nonadjacent angles formed from the intersection
of two straight lines. These angles have equal
measure. The angles we are given are
adjacent angles, so they cannot be vertically opposite angles.
Finally, we know that the answer
cannot be neither, since we have shown that the two angles given in the figure are
complementary angles, since their measures sum to 90 degrees.