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Supplementary and Complementary Angles - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees. Supplementary and complementary angles do not have to be adjacent (sharing a vertex and side, or next to), but they can be.

Two concepts that are related but not the same are supplementary angles and complementary angles. The difference is their sum.
Supplementary angles are two angles whose measures sum to a 180 degrees and complementary are the sum have to add up to 90 degrees. And I noted here that these do not have to be adjacent. So supplementary angles could be adjacent so if I had angles one and two those two would be supplementary. But I could also say if we had some angle here that we said three and let's say 3 was equal to 60 degrees and I had some other angle over here, let's say angle four was equal to 120 degrees, I could say that these two angles three and four are supplementary because they sum to 180 degrees.
The same is true for complementary angles. Let's look at a specific example where you might be asked to identify supplementary angles and complementary angles. Here we have five angles; 1, 2, 3, 4 and 5 and we're told that this angle 3 is 90 degrees, now one thing that you can assume is that 1, 2 and 3 are all linear, so if you add up 1, 2 and 3 it would be 180 degrees, which means that 1 and 2 must also sum to 90 degrees so I could label this as a right-angle. So complementary angles could be angles 1 and 2. So I could say angle 1 and angle 2.
Now, a supplementary pair could be angle 4 and angle 5 which are adjacent and they are linear. So notice that for a supplementary and for complementary you can't say that five angles are complementary but we're always talking about pairs or two's. So remember that when you're trying to evaluate your problems that supplementary sum to 180 degrees or they're linear and complementary angles sum to 90 degrees.

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