Everyone, welcome back. So, 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 going to use what we know about complementary and supplementary angles to solve. This isn't a triangle, but we can still use those same ideas to solve this problem here. We're going to solve for each of these angles below. Alright? 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 180 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 180. So, I can set up an equation here, which is I'm literally going to take those two things and add them together and set them to 180. So, 50-2x+(17x-20). When I combine those two things, I should get 180 degrees. Alright?

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 twenty. The negative 2 combines with the 17. So what's 50 and then +-twenty? When you combine those two things over here, you'll just get that that's 30. And then what happens to the negative 2 and the 17x, that thing just combines to 15x. So when you add those two things, you should get 180. And again, we just subtract 30 from both sides, to get x by itself. So subtract 30 over here. And what you'll see here is that 15x=150. So how do I solve for this? Just divide by 15 on both sides. So divide by 15, and you'll see that x=10. Alright. 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 for those angles. It's not enough to just figure out what x is, you might think that you're just done, but you actually have to go back and actually solve for those angles. Alright?

So then how do we do this? Well, 17x minus 10 minus 20 is going to be 17 times 10 minus 20. And if you work this out, that's 170 minus 20. So in other words, that's going to be 150 degrees. Alright? That's what this angle ends up being. So I'm going to sort of highlight this in blue like this. So this blue angle over here is going to be 150 degrees. Alright. So now you can go ahead and plug in x equals 10 into this equation, or what you can do is you can just say, well, if this is 180 degrees, then that means that this has to be 30 degrees over here. Right? Because 150 and 30 have to add up to 180 degrees. Alright? 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 - 2x, you would see that this actually gets you 30. Alright. So let me know if you have any questions, but this is the correct answer. These two angles over here are 150 and 30. Let me know if you have any questions. Thanks for watching.