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let's do a couple of examples dealing with angles between parallel lines and transversals so let's say that these two lines are parallel so I can label as being parallel that tells us that they will never intersect and they're sitting in the same plane and let's say I have a transversal right here which is just a line that will intersect both of those parallel lines and I were to tell you I were to tell you that this angle this angle right there is 60 degrees and then I were to ask you what is what is this angle right over there you might want me to see well that's very difficult that's on a different line but you just have to remember and the one thing I always remember is that corresponding angles are always equivalent and so if you look at this angle up here on this top line where the transversal intersects the top line what is the corresponding angle to where the transversal intersects this bottom line well this is kind of the bottom right angle you can see that there's one two three four angles so this is on the bottom and kind of to the right a little bit or maybe you could kind of view it as the southeast angle if we're thinking in directions that way and so the corresponding angle is right over here so the corresponding angle is right over there and they're going to be equivalent so this right here is sixty degrees now if this angle is 60 degrees what is the question mark angle well the question mark angle let's call it X right the question mark angle plus the 60 degree angle they go halfway around a circle they are supplementary they will add up to 180 degrees so we could write X plus 60 degrees is equal to is equal to 180 degrees and if you subtract 60 from both sides of this equation you get X is equal to X is equal to 120 degrees so X is equal to 120 degrees and you could keep going you could actually figure out every every angle form between the transversals and the parallel lines this is 120 degrees then the angle opposite to it is also 120 degrees if this angle is 60 degrees then this one right here is also 60 degrees if this is 60 then its opposite angle is 60 degrees and then you could either say that hey this has to be supplementary to either this 60 degree or this 60 degree or you could say that this angle corresponds to this 120 degrees so it is also 120 and make the same exact argument this angle is the same as this angle so it is also under 20 degrees let's do another one let's say I have two lines let's say I have two lines here so it's one line let me do that in purple and let me do the other line in a different shade of purple let me darken that other one a little bit more so you have that purple line and the other one that's another that's a blue or something like that and then I have a line that intersects both of them we draw that a little bit straighter you see if I can draw that a little bit straighter so let me do it in a little let me draw it like that and let's say that this angle this angle right here is 50 degrees and let's say that I were also to tell you that this angle right here is 120 degrees now the question I want to ask here is are these two lines parallel is this magenta line and this blue line parallel so the way to think about it is what would have happened if they were parallel if they were parallel then this and this work or it would be corresponding angles and so then this would be so then this would be fifty degrees this would have to be fifty degrees we don't know so maybe I should put a little asterisks there to say we're not sure whether that's fifty degrees maybe put a question mark this would be 50 degrees if they were parallel but this and this would have to be sub complementary actually regardless of what are a supplementary they would have to add up to 180 degrees actually regardless of whether the lines are parallel if I just take any line and I have something intersecting this angle if this angle is 50 and whatever this angle would be they would have to add up to 180 degrees but we see right here that this will not add up to 180 degrees 50 plus 120 adds up to 170 so these lines aren't parallel another way you could have thought about it I guess this would have maybe been a more exact way to think about it is look if this is 120 degrees this angle right here has to be supplementary to that it has to add up to 180 so this angle do it in this screen this angle right here has to be 60 degrees now this angle corresponds to that angle but they're not equal the corresponding angles are not equal so these lines are not these lines are not are not parallel