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# The angle game (part 2)

## Video transcript

welcome back let's do a couple more angle game problems and and hopefully this will make you an angle game expert so let's start I have the star drawn again and let's say we know the following angles we know this angle right here is 41 degrees 41 degrees we know this angle here is 113 degrees 13 degrees we know this angle here is 101 degrees 101 and what we need to figure out this is the goal of this angle game we want to figure out what this angle is and like always I encourage you to try it on your own pause the video and then you know just try to work it through and if you get stuck then play the video again and and hopefully I'll have a solution for you so pause right now but otherwise let me explain how to do this so let's see we know this this and this we're going to figure out this angle how can we figure out this angle what are possible strategies well if we knew this angle here we could say they're supplementary that angle seems like a hard angle to figure out too because it's not a part of any triangles but this angle is a part of of this triangle right here right so if we were able to figure out this angle and this angle these green angles if we're able to figure out these green angles then we could figure out this brown angle which is the goal of this angle game so this could also be a good time to follow us because I just gave you a hint but let's see this green angle well it's it's supplementary to this angle right here so that means it adds up to 180 degrees and that's clear because it's on kind of the same line so this is 101 degrees and this is going to be 79 degrees right because it adds up to 180 degrees that's 79 now how can we figure out this angle well it's kind of left by itself out in the corner of some place so you know we could see if it's part of any triangles well we already said it's part of this triangle but that doesn't help us because we don't know this angle and that's actually our goal what other triangles is it a part of what's a part of this triangle right here that's why I like the star problem because it has all these triangles in it that might not be obvious to you the first time you look at it but more you look at you see all these triangles so it's part of this triangle and it's also part of this triangle and I'm going to draw this triangle in another color because I think it'll be clear to you that this is a useful triangle to see that it's a part of it's part of this triangle there you go so we have that triangle so do we know two of the angles of that triangle well sure we know this angle and we know this angle so we know that this angle plus 113 plus 41 is going to equal 180 degrees because they're the three angles of a triangle so let's let me call this I don't know G for green a whoops I haven't switched out of my so let's call this G for green so we know G plus 113 degrees 113 that's this one right here plus 41 41 remember we're looking at this triangle that's hardest part just keeping track of which triangle we're looking at is going to equal 180 degrees G Plus what is this 154 all right 40 50 or 154 is equal to hundred eighty degrees that's always where I mess up on the addition and so G is equal to what it says 26 degrees right because I just subtract 154 from both sides 26 degrees so we're almost there so we figured out G we know this green angle we just have to figure out this and they're all part of this triangle the small one right here this small triangle so our goal which is let's call this X X plus G which is 26 degrees which just figure that out 26 Plus this angle 79 all right we figured that out because it was supplementary to this angle it's going to equal 180 degrees so X plus what is this 105 is equal to 180 so X is equal to 75 degrees if I did my addition and subtraction correctly so X is equal to 75 degrees and then we are done let's do another one of these problems and these problems were all generated on the Khan Academy website dynamically by the computer whoever wrote this this software must must genius anyway back to the problems clear inverted colors let me draw some more this is going to be a pretty straightforward drawing it's pretty much just two triangles next to each other like that let me draw another line it goes like that line it goes like that and I think I am done my drawing there you go I am done my drawing so let's see what do we know about this triangle and what do we need to figure out so I'm going to tell you that this angle here this big angle here is 86 degrees 86 degrees we also know that this angle here is 28 degrees 28 degrees and we also know that this angle here is 122 degrees and our goal our mission in this round is to figure out what this angle is and maybe we can do it we do it in a good color maybe we can do it in a couple of different ways so one thing we could do is we could figure out what if we could figure out what this angle is then we could just subtract this green angle from 86 and we would get our answer well this angle is easy right because we know two angles of this triangle so we could figure that out let's just call this item let's call this Y so Y plus 120 222 plus 28 degrees it's going to equal 180 so Y Plus this 150 is equal to 180 so Y is equal to 30 degrees right so this is equal to 30 degrees it's equal 30 degrees so this is 30 degrees and this big angle here is 86 so our goal let's call that X X so X is going to just be equal to the big angle 86 - this angle we just figured out - 30 so X is going to be equal to 50 degrees done that was a pretty straightforward problem let's see if we could figure that out any other way well we could say instead of doing it that way let's forget like we just solved it that way we could say this angle here is supplementary to this 122 degree angle right so it has to add up to 180 so this plus 122 is 180 so what does that make this it makes this 50 58 degrees right this Plus this is going to be 180 so we figured out this if we could figure out this that we could use this triangle how do we figure out this angle well we could look at this big triangle here big triangle here and we know this side right we know this side we could figure out this let's call this Z so we know that Z Plus this angle plus 28 plus this big angle plus 86 is equal to 180 so Z plus what is this 106 114 is equal to 180 so Z is equal to what is this 66 degrees I don't know if I'm doing my math correctly but let's just hope Z is equal to 66 so this is so Z is 66 this angle is 58 and now we can use this triangle here to figure out what this angle is our X so X plus 66 plus 58 is equal to 180 so I already think I might have made a mistake someplace in the Edition so this time around I get X is equal to let's see 66 was 58 is 110 plus 14 is 180 minus 124 so now I got it equal to is equal to 56 degrees oh great I actually got the right answer I was looking at this I thought it was 50 but this was 56 right 86 minus 30 so X is equal to 56 degrees again so we did two different ways so that's what I wanted to show you there's actually not a right answer as long as you kind of get there eventually and we solved it two different ways and I did all my addition subtraction correctly and and you get the exact same answer so hopefully you'll you find the angle game fun and you'll be playing this with your friends I'll see you later