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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 degree 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 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 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 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 it was 194 - 182 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 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 nine times negative six which is negative 54 plus 194 this also equals 140 degrees