Complementary and Supplementary Angles - Video Tutorials & Practice Problems

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concept

Intro to Complementary & Supplementary Angles

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Everyone. Welcome back. So in some problems, you may be asked to find what are called complementary or supplementary angles. These are words you may have heard at some point in a math class, but we'll be working a lot with them when it comes to angles and triangles. I wanna make sure you have this down really well. So I'm gonna show you in this video that these are just two fancy words to describe the idea that angles have to add up to two special numbers, complimentary angles add up to 90 degrees and supplementary angles add up to 100 and 80. So these are just fancy words to mean 91 180. We'll do a bunch of examples together. Let's get started here. All right. So complimentary angles form 90 degrees. We know from the corded system that it's zero and this is 90. So if I have some given angle, right? Like 30 degrees, how do I find the compliments of that angle? Well, basically, this just says that two angles, theta one and theta two have to equal 90. Now don't worry about the theta one and theta two that much because usually these problems, one of the angles is already gonna be given to you. So what do we have to add to 30 to get to 90? I just have to add 60. Another way to do this is 90 minus 30 will give you 60 degrees. That's sort of like a shortcut way of using this equation. All right. That's really all there is to it for supplementary angles. It's a very similar idea, except now we have to add not to 80 not to 90 but 100 and 80. All right. So if I go from 0 to 90 that's like halfway uh of, you know, that's a quarter of, of a circle. But if I go another quarter like 90 this means that the straight line is gonna be 100 and 80 degrees. All right. So if I have an angle like 30 what's the supplement of that angle? I just have to figure out another angle that adds to it to get me to 100 and 80. So 180 minus 30 give me the supplements of that angle which is 100 and 50 degrees. So those two angles, 1 50 30 are supplementary. That's really all there is to it. Now, there's a sort of like a mnemonic that I used to help remember this, which is that complementary angles form corners. So C with C and supplementary angles form straight lines. So S with S right. So complementary corners, supplementary straight. That's really all there is to it. Let's go ahead and get some examples. All right. So we have the, uh, we're gonna find the compliments and supplements of these angles here that are given to us. We've got 20 degrees. All right. So we've got our equation over here again. Don't, don't pay attention to the theta one, theta two because all you have to do is just think about what angle do I have to add to 20 to get to 90. So if you wanted to sort of set this up, if you couldn't do this in your head, you would just say theta plus 20 equals equals 90. And then you would just uh knock off 20 from both sides, right? So knock off 20 knock off 20 you're gonna get the theta is equal to 70. So the complement of 20 degrees is 70 degrees. Very similar with uh a supplement except now you're gonna have to add up to 100 and 80 right? So theta plus 20 equals 180 subtract 20 from both sides over here. When you'll see that data is equal to 160. So that's the supplement of this angle. All right, that's really all there is to it. So let's take a look now at the second example over here 100 degrees. What do I have to add to 100 degrees to get me to 90? That's kind of weird. Because if you were sort of visualize this, 100 degrees is gonna look something like that. So I have to have, I'd actually have to go backwards and add a negative angle to get to 90. And that's kind of weird. So what she needs to remember is that complementary angles and supplementary angles are always assumed to be positive. So what that means here is that 100 degrees actually has no compliments because you'd have to add a negative angle. So the complementary angle of the 100 degrees doesn't exist. However, it does have a supplement because remember that, what do I have to add to 100 to get me to 180? I just have to get I have to add 80 degrees. That's all there is to it. All right. So pretty straightforward concept. Uh Let me know if you have any questions. Thanks for watching.

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Problem

Problem

Find the complement & supplement of a $45°$ angle.

Complement: ____

Supplement: ____

A

$Complement=135\degree;Supplement=45\degree$

B

$Complement=45\degree;Supplement=135\degree$

C

$Complement=315\degree;Supplement=135\degree$

D

$Complement=45\degree;Supplement=315\degree$

3

concept

Solving Problems with Complementary & Supplementary Angles

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Hey, everyone. Welcome back. So in a previous video, we learned complementary angles add up to 90 degrees and supplementary angles add up to 100 and 80. But some problems like the one we're gonna work out down here will throw at you some shapes or diagrams or even triangles that will have the angles that are written in terms of variables like X. They won't give you an angle and ask you for the compliment or supplement, they'll give you something like this. Now, it might seem like we have to use a different method to solve these types of problems, but we actually use what we know about complementary and supplementary angles to solve them. Let me just go, go ahead and show you using this example over here, we'll walk through it together and I'll show you how this works. All right. So this is a right triangle over here, we have a right triangle with this little square in the corner. That means that that's 90 degrees. So how do we solve this problem here? Up until now whenever we have triangles, we usually have what two of the angles are we can solve for the other one because we know all the triangles and all the angles in a triangle add up to 100 and 80. Well, the whole idea here is if this is fixed at 90 degrees in a right triangle, because one angle is fixed at 90 the other two angles over here, these two have to also be 90. So those two angles are also going to be complementary. So how can we use this to help us solve this problem? Well, basically we know that whatever these two angles are, they have to add up to 90 degrees. So we can set it up just like we set up an equation for complimentary angles. So X plus X plus 10, those two things, if I put them together, they have to add up to 90 degrees. Now we can do is we can just solve this like any other linear equation I can combine like terms. This ends up being two X plus 10 equals nine, subtract 10 from both sides over here, we're gonna get the two X is equal to 80 when you divide by two, for both sides, which you'll see is that X is equal to 40 degrees. All right. So X is equal to 40. Are we done here? Is that just the answer? Well, not quite because the question asks us to find what each of the angles are in the triangle below. It's not enough to find just what X is now, you actually have to plug it back into those angles to solve for those. All right. Now, for this over here, just because it's X, we actually know that this is already gonna be 40 degrees. And then what we can do is we'll say, well, what's X plus 10? That's just gonna be 40 plus 10. Some of the words, this is 50 degrees. We know these two angles are complimentary, 4050. They both add up to 90. So now that's our whole triangle. All right. So these are your angles. We have 50 degrees, 40 degrees and 90 degrees. All right. All the angles have to add up to 180 we can use complimentary angles to solve for this. Hopefully, that makes sense. Thanks for watching.

4

example

Example 1

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3m

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Everyone. Welcome back. So uh let's take a look at this example over here because we're given a straight line with some angles and these angles are actually given to us in terms of variables like X. So we're gonna use what we know about complementary and supplementary angles to solve. This isn't a triangle. We can still use those same ideas to solve this problem here. We're gonna solve for each of these angles below. All right. How do I do that? Well, I've got a straight line like this and I've got these two angles over here and what we know about supplementary angles is that they will always add up to 100 and 80 degrees. So in other words, if I take this angle, whatever it is and I add it to this angle, whatever that is, those things have to add up to 100 and 80. So I can set up an equation here, which is I'm literally gonna take those two things and add them together and set them to 180. So 50 minus two X plus and this is gonna be 17 X minus 20 when I combine those two things I should get 100 and 80 degrees. All right. So how do we solve these types of equations? This is really just a linear equation we've dealt with these before in previous videos. The idea here is that you just combine like terms. So the 50 combines with the negative 20 the negative two combines with the 17. So what's 50? And then a plus negative 20? And you combine those two things over here, you'll just get that, that's 30. And then what happen to the negative two? And the 17 X, that thing just combines to 15 X. So when you add those two things, you should get 100 and 80. And again, we just subtract 30 from both sides um to get uh X by itself. So subtract 30 over here. And what you'll see here is that you get 15, X is equal to 150. So how do I solve this? Just sort of divide by 15 on both sides? So divide by 15 and you'll see that X is equal to 10. All right. So is that it is X equals 10? And I'm just done. No, not quite because what you have to do is you have to plug these numbers back into or you have to plug this X equals 10 back into these equations to solve those angles. It's not enough to just figure out what X is. You might think that you're just done. You actually have to go back and actually solve those angles. All right. So then how do we do this? Well, 17 X minus 10 minus 20 is gonna be 17 times 10 minus 20. And if you work this out, that's actually 100 and 70 minus 20. So in other words, that's gonna be 100 and 50 degrees. All right, that's what this angle ends up being. So I'm gonna sort of highlight this in. Uh I'll highlight this in blue like this. So this blue angle over here, is it gonna be 100 and 50 degrees? All right. So now you can go ahead and, and plug in X equals 10 into this equation or what you can do is you can just say, well, if this is 100 and 80 degrees, then that means that this has to be 30 degrees over here, right? Because 100 and 5030 have to add up to uh 100 and 80 degrees. All right. So you really actually have to plug this back into just one of the equations and then you can solve for the other one. However, if you were to plug this back into 50 minus two X, you would see that this actually gets you 30. All right. So uh let me know if you have any questions, but this is the correct answer. These two angles over here are 100 and 5030. Let me know if you have any questions? Thanks for watching.