 In this video, I'm going to talk about finding the complement and the supplement of different angles. These are just a few examples of the difference between complement and supplement. Okay, so first off, I want to go over real quick just the vocabulary, complement, and the vocabulary supplement. Compliments, now when you say complement and supplement, you're talking about angles. Okay, we're talking about the plural form, angles. So we're talking about two. So if I want to find complement angles, complement angles, it's two angles that add up to 90 degrees. Compliment is two angles that add up to 90 degrees. Okay, so that's the vocabulary for complement. Supplement angles, okay, supplement angles, again two angles here, are two angles that are going to add up to 180 degrees. Okay, so you've got to keep those two separate from one another, but you also have to understand it's two angles, pairs of angles, two angles that add up either to complement 90 degrees or supplement 180 degrees. So you've just got to keep another difference between the two. Okay, first example here, find the complement of angle F, okay, just a small little picture that we have here. This angle is 59 degrees, so I want to find the complement. Okay, so now the thing is, when we talk about complement angles, again, complement is going to be, right up here, it's going to be 90 degrees. It's going to be two angles, two angles that add up to 90 degrees. Okay, so find the complement of angle F. This is actually, what they're doing is they're telling you what one of the angles is. They're telling you what one of the angles are, I think that's what the proper English is. Anyway, so you've got to find out what the other angle is. So again, we've got to take an angle plus an angle, and they should add up to 90 degrees. Okay, so this kind of looks like a formula that I'm using here, but I'm just kind of using this as a diagram. All right, so now the thing is, we actually know what one of these angles is. One of these angles is 59 degrees, plus this other angle, I don't know what that other angle is. So actually what I can do is I can use a variable here, so we use the variable A, why not, equals 90 degrees. All right, so what I need to do is I need to find out what that missing angle is. This is going to be the complement of F. All right, so what I do is I just take this 59, and again, it's just an algebra equation, so I take this 59, subtract it over to the other side, my missing variable, my missing angle is going to be, one gets this to 60, 30 gets this to 90, so this is going to be 31 degrees. All right, so the complement of F, comp of angle F equals 31 degrees. Okay, so notice that for my answer, I kind of spell it out, the complement using an abbreviation, your complement of angle F is equal to 31 degrees, I want to make sure and answer the question, because this A equals 31 degrees, nobody's not going to know what A means, that's just a random variable that I picked, so make sure that you actually answer your question. Okay, so there's complement, there's an idea of complement, so now for the second example, supplement of angle G, if the measure of angle G is 107 degrees. Now notice we've got no picture here, okay on this previous problem we had a nice little picture over here, we know what the angle was, but what this problem is designed to tell us, is that you don't necessarily, you don't necessarily need a picture to find out what a complement or a supplement is, so supplement are two angles, two angles that add up to 180, 180 degrees, so again I have, kind of like last time, I'm going to start with a kind of a, kind of a scaffolding for my equation, so I have an angle plus an angle is going to be equal to 180 degrees. Now if I, I know what one of those angles is, angle G is going to be 107 degrees, so just like last time, 107 plus some angle we'll call it B is equal to 180 degrees, so what I want to do is I want to find that missing angle, but notice here I'm using a couple different variables, I'm using A's, I'm using B's, it doesn't really matter what variables you're using, I'm just throwing in variables, because that's what a variable is, it's an unknown, it could be a lot of different numbers, in this case it's only going to be one number, but you can use whatever variables you want to, so I'm just throwing in variables, because this is my missing angle, right here that's my missing angle, I want to find out what that is. Alright so just like last time, I'm going to solve this like I would in any algebra equations, 107, subtract that over to the other side, that's going to be 73, so in this case the supplement, abbreviate supplement, SUPP, supplement of angle G is 73 degrees, equals 73 degrees, there we go. Alright and again make sure you answer the question, just don't give me, just don't give any of your teachers B is equal to 73 degrees, because that makes no sense, B, there's no B in this problem, okay, that doesn't make any sense, so make sure you actually answer the question. Alright, down to my third and final example, when we change colors here a little bit, so we don't mix these together, don't mix these together. Alright so the supplement of angle X, find the supplement of angle X, so just like the last one, two angles I add up to 180 degrees, now when I look at the picture of this one, I get an expression, 7A plus 10, what is that? It doesn't really matter, it doesn't really matter, it could be a number like it was for these last two, or it could be a variable expression, it doesn't really matter. Okay now these type of problems tend to confuse students because as we'll see here in a little bit, you're not going to actually find a final answer, you're not going to find a nice clean number like 31 or 73, you're not going to find that, you're going to find something a little bit different, and that on the other hand for students is kind of confusing because usually in mathematics you find one nice neat answer, in this case you're not really going to find a nice neat answer. Okay but anyway we're going to do this just like we did the last problem, supplement is an angle plus an angle, and when you add them together you get 180 degrees, okay just like last time. Okay so now what I'm going to do is I actually know what one of those angles is, one of those angles is 7A plus 10, 7A plus 10 plus, I don't know what the second angle is, so I'm going to use an x this time, so a variable x this time. Okay so I know what one of the angles is 7A plus 10 plus the second angle, which I don't know just keep it as x, if I add those together I should get 180 degrees again because they are supplement angles. Okay so now again I'm just going to solve this just like I did just the rest of them. Now if I look at the other problems, the unknown that I had, all I did was I got that by itself and I basically got my answer, so in this case the A got it by itself, I got 31, over here the B was by, I got B by itself and I got my answer, I'm going to do the exact same thing here, which again is going to be a little bit confusing because we have this other variable, we have an A over here. Okay but again don't worry about that, I'm trying to figure out what this missing angle is. This doesn't matter over here, this A doesn't matter, I only care about this x, this is the missing angle, this is the supplement of angle x, that's what I'm looking for. Now did I think of it? x is a very bad, very, very bad variable to use, so in this case I'm actually going to go backwards, I'm going to backtrack just a little bit and I'm going to get rid of this x and I'm going to come back in, let's not use x, let's use z. Okay so my apologies there, I should not use that variable x because you might mistake it for this angle here which it's not so I'm going to change that around a little bit. But again same thing, first angle is 7A plus 10, the second angle I don't know what it is but when you add them together you do get 180 degrees, I want to figure out what this angle is so I have to get this one by itself. So this 7A plus 10, I'm going to subtract both of these over to the other side. So z is equal to 10 subtracted over is going to be 170, 7A subtracted over is a negative 7A and then that's that's it, these two, that's a number and a variable, they're not going to combine so you can't combine those two, don't try to bring them together and that's basically it. So just like the rest of them, just like my last two problems, the supplement using a little bit of abbreviation here, the supplement of angle x is 170 minus 7A degrees, well parentheses degrees. That right there, that right there, you're going to look at that, that's going to be very confusing because you're thinking to yourself well the previous problems we got 73, we got 31, why do we get an expression for an answer? Well that's kind of how it works since they, the only thing that they gave us was an expression, they don't tell us what A is, they don't give us any other information about any angles that might be the same, anything like that so that's it, that's as good as it gets and that can be a little confusing for when you see that for the first time but just, just remember, just remember that I just need to solve for this angle right here, so I name it whatever you want to don't name it x like I did, so angle z, I need to find out what that is so solve for that, get everything else on the other side and then that's what the angle is going to be. If you happen to figure out what A is, if you happen to figure out A is 12 or 52 or whatever it is then you could very easily plug that number in and figure out what the supplement is going to be but in this case we're just going to leave it just like that. Okay so hopefully those three examples helped you out with the difference between complement and supplement, just to rehash a little bit, complement is when two angles add up to get 90 degrees and supplement is when two angles add up to get 180 degrees so you know the difference between the two. Hopefully these couple of examples helped you understand the difference between complement and supplement angles.