How to Find Measures of Supplementary Angles

Identify and find measures of complementary and supplementary angles.

In this lesson, let’s learn about complementary and supplementary angles. We’re given a protractor and a diagram and we need to tell whether the angles given to us are complementary, supplementary or neither. So let’s look at the first two angles, DXE and AXB, DXE is this angle right here, and AXB is this angle, AXB, which is right here. Since we are given the measurements, I want to see what the measure of this angle is. It goes from 0 to here, so this measure is actually between 50 and 60. So this is 55 degrees. So angle DXE is 55 degrees. Angle AXB, we need to measure. I go from 0, it goes to 35. This is still 35 degrees. Now, since the sum of both of these, 55 plus 35 is 90 degrees, then these are complimentary angles. Remember that complementary angles, which means total 90 degrees. These two sum equals 90 degrees. If the sum equals 90 degrees, they are complementary. Let’s look at the second problem. DXE—so this is part A, part B, I'm going to do in green. Part B says angle DXE, which we know is 55 degrees. BXC, this is what we need to find out. BXC is this angle right here. Well, how do I measure this one? I have got an easy way to do it. Let’s measure this angle first. So this is angle BXE, I know, because I could start at 0 and go all the way to 145 degrees. I can now subtract from this angle, which I will be left with just the part that we are looking for. This is angle is CXE. CXE is 0 to 105. So when I subtract these two, I get BXC equals, instead of a question mark, BXC equals angle BXE minus angle CXE equals 145 minus 105 is 40 degrees. So the two angles are 55 and 45. Their sum is 95 degrees. 95 degrees means they are neither. For them to be complementary, they have to be 90 degrees. For them to be supplementary, they have to be 180 degrees. The sum of these two angles give to us is 95 degrees. This is 95 degrees. This is 90 degrees. Let’s look at the third one, which is, I'm going to use black, AXC. What’s the measure of AXC? Start with 0, we go 75 degrees. This is 75 degrees. And CXE is this one. CXE, we just computed as 105 degrees. Well, I actually don’t have to even add them. As we can see, both the black arrows covers the entire piece, which means they cover a straight line. But anyway, 75 plus 105 is 180 degrees. So part C is a 180 degrees is the sum of angle AXC plus angle CXE, which means they are supplementary. Supplementary is 180 degrees. Complementary is 90 degrees. So now that we have done the first question, let’s try the second one. Angles A, X and Y are supplementary. I'm going to ‘stroll’ that. Angle X and Y are supplementary, which means sum equals 90 degrees. If measure of angle X is 65,whats the measure of Y? So if the sum is 90 degrees, that means measure of angle X plus measure of angle Y should be 90 degrees. Measure of angle X is given to us as 65 degrees, plus measure of angle Y equals 90 degrees. When I solve this, I take away 65 from both sides, I get measure of angle Y, is 25 degrees. That’s what we are looking for. Key thing to remember; complementary angles, sum 90 degrees. Supplementary angles, sum 180 degrees.