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CCSS.Math:

so we have two intersecting lines here and then we have this other purple looking line and then they've given us some angles they tell us that this the measure of this angle right over here 7x the measure of this angle right over here is 60 degrees and the measure of this angle right over here is X so let's try to figure out what all of these angles are so to do that we have to figure out what X is and there's a big clue here because 60 plus the 60 degree angle plus the X angle their adjacent and if you add these two angles together their outer raise our vertical angle with this 7x angle so we could say and just to visualize that a little better let me color it in so you see that this let me do it this way you see you see that this angle out here we do in a color I haven't used yet this entire angle right over here which is going to be 60 degrees plus X that's a vertical angle with this angle the one that has measure 7x so we could say that 60 degrees plus X is equal to 7x because vertical angles are equal so let's write that down we get 60 and we'll assume that everything is in degrees 60 Plus let me do that in this other color 60 plus X is going to be equal to 7x and now we just have to solve for X so the simplest thing to do would be to get all of our X's on one side of the equation I've already gotten seven X's on this right-hand side so let's bring let's get let's get rid of all of the X's on the left-hand side and the easiest way to get rid of this X is to subtract X from the left hand side but in of course in order to keep it an equation we can't just do something to one side otherwise it won't be equal anymore we have to do it to both sides so let's subtract X from both sides and on the left hand side we are left with just the 60 so we're left with just a 60 and then that is going to be equal to 7x minus X I have 7 of something and I get rid of one of them I'm going to have 6 of that something left so that's going to be equal to 6x so we have 6 times something is equal to 60 you could probably figure that out in your head but I will do a little systematically we can divide both by 6:00 to solve for X so let's do that and we would be left with X is equal to 60 divided by 6 is 10 and we reminded ourselves that everything was in degrees and we could even do that here this was in degrees this is in degrees and so this is in degrees right over here so the measure of this angle right over here is 10 degrees so this one right over there is 10 degrees this is of course 60 degrees you add them together 60 degrees plus 10 degrees is 70 degrees so this bigger angle right over here is 70 degrees and of course this one over here it's a vertical angle it's going to have to be the same and we see that 7 times X 7 times 10 degrees is 70 degrees as well