Question Video: Classifying Pairs of Angles Mathematics

Video Transcript

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 right angle.

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 degrees.

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.