 In this video, we provide the solution to question number 14 for practice exam 1 for Math 1060. We're given the following geometric diagram that you see right here and we're asked to find the variables x and y. So what are some things I know about this? Well, first of all, I see there's some unknown angle here that depends on x and there's some unknown angle right here that depends on y. But when I look at the two angles together, they form a flat line. We see it right here. And so these angles are in fact supplementary angles. That means if I take 5x plus 20 degrees and I add that to 2y plus 45 degrees, that's going to equal 180 degrees. They're supplementary angles. Therefore, the sum of the two angles will give us 180 degrees. So let's see what we can do with this equation right here. Combining like terms of some kind, I mean, you have these x's and y's. You really can't combine those together yet. You have 5x plus 2y. Of course, you get 20 plus 45. That's going to be 65. That's equal to 180. So we can of course subtract from 180 the 65 right there. That of course gives us 5x plus 2y is equal to 115. But now we have two variables x and y. So there's really not much more we can do with that. Maybe we can find some more information in this problem. Another thing to notice here is that we have this triangle right here, this triangle. We know that the sum of the three angles of a triangle add up to 180 degrees. And you'll notice that each and every one of these angles only involves the variable y. So maybe that's what we do with next here. If we take 4y degrees plus 2y plus 45 degrees plus 2y plus 15 degrees, this is going to equal 180 degrees. So this time we want to solve for y because there's no x in play right here. If you take 4y plus 2y plus 2y, if you add like terms, you're going to get an 8y right there. You have 45 degrees plus 15 degrees. That's going to add up to be 60 degrees. That's equal to 180. If we subtract 60 from both sides, we get 8y is equal to 120. And if you divide both sides by 8, you're going to get y equals 15. All right, so we get y equals 15. Then we can use this substitution into our equation down here for this unknown x and y. We now know y. So we're going to get 5x plus 2 times 15. 2 times 15, of course, is 30. So we get 5x plus 30 is equal to 115. So track 30 from both sides. We get 5x is equal to 85. And then if we divide both sides by 5, we'll get x is equal to 17. Thus, we were able to solve this problem here. x is equal to 17 and y is equal to 15.