How To Figure Out Complementary And Supplementary Angles

​Complementary​ and ​supplementary​ are terms used to describe special relationships between two angles. If any two angles are complementary, their measurements add up to a total of 90 degrees or, to put it another way, their measurements add up to a right angle. If two angles are supplementary, their measurements add up to a total of 180 degrees or a straight line/straight angle. If you know the measurement of one of these angles, you can use the complementary or supplementary relationship to find the measurement of the other angle.

Because the sum of two complementary angles is 90 degrees, if you're given the measurement of one angle ​x​, the measurement of its complementary angle is 90 – ​x​ degrees.

So if you're told that an angle measures 30 degrees and asked to find its complement, you could calculate:

\(90\text{ degrees}-30\text{ degrees}=60\text{ degrees}\)

The measurement of the missing (complementary) angle is 60 degrees.

Check your work by summing the measures of the two complementary angles. In this example, you have:

\(30\text{ degrees}_60\text{ degrees}=90\text{ degrees}\)

If both angles add up to 90 degrees, you did indeed find the complement of the first angle.

Because the sum of any two supplementary angles is 180 degrees, if you're given the measure of an angle ​y,​ then you can find its supplement or supplementary angle by calculating 180 – ​y​.

So if you are told that one angle measures 124 degrees and asked to find its supplement, you would calculate:

\(180\text{ degrees}-124\text{ degrees}=56\text{ degrees}\)

The measure of the missing angle is 56 degrees.

Just as with complementary angles, you can check your work by summing the two angles you just computer. In this case you have:

\(124\text{ degrees}+56\text{ degrees}=180\text{ degrees}\)

If the two angles total to exactly 180 degrees, they are supplementary.