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# Angles (part 2)

## Video transcript

so let's review everything that we know so far because it's good to keep reviewing just so because these are things you should never forget the rest of your life so if I have a line and if I draw an angle that goes 300 let's say this is the pivot point right if I go all the way around the line or in a circle that's 360 degrees 360 degrees or we learned that there 360 degrees in a circle right we also learned that if I have lines like this if I have if I have two angles draw like that and this is angle X this is angle Y X and y are supplementary supplementary and that just means that they add up to 180 degrees X plus y is equal to 180 degrees and why does that make sense because look if we go if we add up X plus y we have gone halfway around the circle so that's 180 degrees right so this is part of the way and this is the rest of the way so X plus y are going to equal 180 degrees so hopefully we have learned that and then let me switch colors for the sake of variety let me use my line tool if I have if I have C I'm going to draw perpendicular lines have that line and then I have that line and they are perpendicular and then I have another I have another line so it goes like that and then I say that this is angle X whoops this is angle X and this is angle Y well I said these the this line and this line are perpendicular right so that means that they intersect at a 90 degree angle so we know this whole thing is 90 degrees 90 degrees and so what do we know about X plus y well X plus y is going to equal 90 degrees it's going to equal 90 degrees or we could say that x and y are complementary and I always get confused between supplementary and complementary you just got to memorize it I don't know if there's any let's see is there any easy way 180 supplementary you could say that 180 100 starts with an O which supplementary does not start with so there 100 say there's your pneumonic complimentary and 90 starts with an N and complementary does not start with an end that's your your other mnemonic a complimentary men complimentary complement spelling it right who cares let's move on so let's learn some more stuff about anything like what I'm going to do is I'm going to give you an arsenal and then once you have that arsenal you can just tackle these beastly problems that I'm going to throw at you so just just take these for granted right now and then in a few videos probably we're going to tackle some beastly problems so if I have and you know I'm using variables here and if you're not familiar verbs you can put numbers here if X was 30 degrees then Y is going to be 60 degrees right or in this case if X is I don't know 45 degrees then Y is going to be 135 degrees that other way let me draw another property of line angles of intersecting lines so if I have two angles two lines that intersect like this so a couple of interesting things so first I'm gonna teach you about opposite angles so if I know let's say that this is let me switch colors let me switch to yellow so this is X this is X degrees then it turns out that the angle opposite to it is also equal to X degrees is also equal to X degrees and you don't believe me well let me prove it to you let's say let's say we don't we don't know that this is let's say we call this I don't know let's call this let's call this y degrees right and I'm going to prove to you that X and the y are the same well what do we know already well we know let's call this other angle and I'm doing this to confuse you let's call this other angle here let's call this angle Z well what do we know about angle X and angle Z it may not be obvious to you because I've drawn it slightly different but I'll give you a small hint with a appropriately interesting color so what angle is this whole thing right here well I'm just going along a line right that's halfway around a circle so what angle is that well that's 180 degrees so what does X plus Z equal well X plus Z is going to equal that larger angle X plus purple Z that's not X plus Z is going to equal and go switch to the blue maybe it's taking too much time for me to switch is equal to 180 degrees or X and Z are supplementary supplementary supplementary I've run out of space so what do we know about Z well Z is equal to 180 minus X right because X plus Z is 180 fine now what's a relationship between Z and Y well Z and Y are also supplementary because look if I drew this angle here look at this big angle look at that angle what angle is that well once again I'm still going halfway around the circle right but now I'm using this line right here so that's 180 degrees so we know that Z angle Z plus angle Y is also equal to 180 degrees Z plus y is also equal to 180 degrees right or you know I don't want to keep writing it but Z and Y are also supplementary but we just figured out that Z is 180 minus X right so let's just substitute that back in here so we get 180 minus X plus y is equal to 180 degrees why don't we subtract 180 degrees from both sides of this equation that cancels out and we get minus X plus y is equal to 0 and then add X to both sides this equation and we get Y is equal to X that was a very long way of showing you something that is fairly simple that opposite angles are equal to each other so X is equal to Y and if you played around with this if you just drew a bunch of straight lines and they intersected at different angles I think it when you eyeball it it would make sense and then similarly Z if that's Z then the other opposite angle here is also this is also Z degrees so what do we know now the total angles in a circle 360 degrees when two angles kind of combined go halfway around the circle or you know that they combine kind of form a line there's different ways you can think about it we know they're supplementary they add up to 180 degrees X plus y is 180 degrees if they add up to 90 its complementary X plus y is 90 and then opposite angles are equal to each other right this angle this angle is equal to this angle and then this angle is going to be equal to this angle for them for the same reason because it's opposite in the next video I'm going to show you about trends parallel lines and transversals more fancy words for what I think are fairly straightforward concepts I'll see you in the next video