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

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**Supplementary** angles are angles whose measures add up to 180°. So, to determine if a pair of angles is supplementary, add their measures together, and determine if their sum is 180°.

**Complementary** angles are angles whose measures add up to 90°. Likewise, to determine if a pair of angles is complementary, add their measures together, and determine if their sum is 90°.

In order to be supplementary or complementary, the two angles do not need to be adjacent (meaning they do not need to share a common vertex and a side). What is important is just the sum of their measures.

Once you’ve learnt about supplementary and complementary angles, you are going to be asked to list them in a problem that’s similar to this. But what are supplementary and complementary angles? Supplementary angles are two angles whose measures sum to 180 degrees.

Complementary angles are two angles whose measures sum to 90 degrees. So two key things here, one they don’t have to be adjacent which means they share a common vertex and a side, and two we are only talking about two angles so this is a pair of supplementary angles and a pair of complementary angles.

Let’s go back to our problem and see if we can identify any supplementary or complementary angles. The first thing that I’m going to do when I look at this problem is say I don’t know two of those angles. So how can I find this obtuse angles and the other obtuse angle.

They are not vertical that is they are not going to be congruent to each other but I can use what I know. I see that’s 70 degrees and this angle form a linear pair which they means that they sum to 180 degrees. Which means that AFB must be 110 degrees, so I could list that as a pair of supplementary angles that is AFB so angle AFB and angle AFE . As long as we are talking about supplementary angles let’s see if there are any other angles here that might sum to 180 degrees.

Well we know that 20 plus this angle plus 15 is 180. 20 and 15 is 35 if you take away 35 from 180 you get 145 degrees. So if I look at different combinations here I did 110 and 70, I already got that 110 plus 145 is not 180 110 and 20 is not 110 and 15 is not 180. So it doesn’t look like there’s any way for me to sum just two angles here besides these two that aren’t listed so we only have one pair of supplementary angles.

Now what about complimentary angles we said those have to sum to 90 degrees and if I look at this I see that 110 degrees and 145 degrees are already more than 90, so I’m going to ignore those two and so I’m left with three 70, 15 and 20 degrees.

There’s only one combination here that will sum to 90 and that’s 70 plus 20, so AFE, angle AFE and angle BFC. So the keys to finding out your supplementary and complementary angles are first remembering which one sums to 180 which one sums to 90 and secondly if you are given a picture find all your angles first then go about identifying your pairs.