Missing angle problems
Let's say we have two intersecting lines. So that's one of the lines right over there. And then I have another line right over here. So those are my two intersecting lines. And let's say we know that the measure of this angle right over here is equal to 7x plus 182. And this is being given in degrees, so it's 7x plus 182 degrees. And we know that the measure of this angle right over here is 9x plus 194 degrees. So my question to you is, what is the measure of each of these angles? And I encourage you to pause the video and to think about it. Well, the thing that might jump out at you is that these two things are vertical angles. They're the opposite angles when we have these intersecting lines right over here. And vertical angles are equal to each other. So we know, because these are vertical angles, that 9x plus 194 degrees must be equal to 7x plus 182 degrees. And now we just have to solve for x. So if we want all the x-terms on the left-hand side, we could subtract 7x from here. We've got to do it to both sides, of course, in order to maintain the equality. And then we could put all of our constant terms on the right-hand side. So we can subtract 194 from the left. We have to subtract 194 from the right in order to maintain the inequality. And on the left, what we're left with is just 2x. And on the right, what we're left with-- let's see. 182 minus 194. So if it was 194 minus 182, it would be positive 12. But now it's going to be negative 12. We're subtracting the larger from the smaller, so it's equal to negative 12. And then divide both sides by 2. And we get x is equal to negative 6. And now we can use that information to find out the measure of either one of these angles, which is the same as the other one. So we can see here that if we take 7 times negative 6 plus 182, so 7 times negative 6 is negative 42, plus 182 is going to be equal to 140 degrees. And you'll see the same thing over here. If we say 9 times negative 6, which is negative 54, plus 194, this also equals 140 degrees.