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# Measures of angles formed by a transversal

CCSS.Math:

## Video transcript

so I've got two parallel lines so that's the first line right over there and then the second line right over here let me denote that these are parallel these are parallel lines to do that a little bit neater parallel lines and then let me draw a transversal so a line that intersects both of these parallel lines so something like that and now let's say that we are told let's say we're told that this angle right over here this angle right over here is 9x plus 88 and this is in degrees and we're also told that this angle right over here is 6x plus 180 - once again in degrees so my goal here and my question for you is can we figure out what these angles actually are given that these are parallel lines and this is a transversal line I encourage you to pause this video and try this on your own well the key here to realize the key here to realize is that these all right over here are related by the fact that this is their form from a transversal intersecting parallel lines and we know for example that this angle corresponds to this angle right over here they're going to be congruent angles and so this is 6x plus 180 - this is also going to be 6x plus 180 - and then that helps us realize that this blue angle and this orange angle are actually going to be supplementary they're going to add up to 180 degrees because put together when you make them adjacent their outer rays form a line right over here so we know that 6x + 180 - plus 9x plus 9x plus 88 is going to be equal to 180 degrees is going to be equal to 180 degrees and now we just have to simplify this thing so 6x plus 9x is going to give us 15 X and then we have 180 - plus 88 let's see 180 - +8 would get us to 190 and then we another eighty gets us to 270 plus 270 is equal to 180 is equal to 180 if we subtract 270 from both sides we get 15 X is equal to negative 90 negative 90 and now we can divide both sides by 15 divide both sides by 15 and we get X is equal to what is this let's see 6 times 15 is that 60 plus 30 is 90 so this is X is going to be equal to negative 6 so so far we've made a lot of progress we figured out what X is equal to X is equal to negative 6 but we still haven't figured out what these angles are equal to so this angle right over here 9x plus 88 this is going to be equal to 9 times negative 6 times negative 6 plus 88 9 times negative 6 is negative 54 negative 50 4 plus 88 let me write this down before I make a mistake negative 54 plus 88 is going to be let's see to go from 50 88 minus 54 will give us 34 degrees so this is equal to 34 and it's in degrees so this orange angle right over here is 34 degrees the blue angle the blue angle is going to be 180 minus that but we can verify that by actually evaluating 6x + 180 - so this is going to be equal to 6 times negative 6 is negative 36 plus 180 - so this is going to be equal to let's see it's 1 let's see if I subtract the 6 first I get to 176 so this is gets us to 146 degrees and you can verify 146 plus 34 is equal to 180 degrees 146 plus 34 is equal to 180 degrees and we could also figure out the other angles from this as well we know that this if this is if this is 34 degrees and this must be 34 degrees as well those are opposite angles this angle also corresponds to this angle so it must also be 34 degrees which is opposite to this angle which is going to be 34 degrees similarly if this one right over here is 146 degrees we already know that this one is going to be 146 this one's going to be 146 since its opposite and that's going to be 146 degrees as well