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# The angle game

## Video transcript

let's play the angle game so I've drawn this crazy figure here and I'm going to give you a couple of angles and then I want you to figure out another angle so let me give you some angles so let's say that this angle up here make sure I'm using the right tool let's say this angle up here that is 56 degrees 56 degrees and then I also tell you this angle here this angle here is 115 degrees 115 degrees and what I would like you to figure out this is the object this is the object of the angle game I want you to figure out what this angle is right here if you are brave you can pause the video and try to figure out yourself if you would like me to walk you through it and maybe I give you a couple of steps and then you pause it and you get the rest of it by yourself but I will now show you how I would have solved this in the angle game and and you have all the tools necessary to already solve it and now I want you to be able to get good at this because this is this is kind of like the key skill in the SAT so let's see oh I didn't give you a key piece and for you're probably saying Sal I can't solve this and it's you probably can't because I haven't given you a key piece of information this line here and this line here so this line and this line they're parallel see I was telling you to solve it before giving your key piece information that means that they are parallel so what can we do with this figure so whenever I see these type of problems either while playing the angle game or on say an SAT I just literally kind of figure out every angle that I can figure out and slowly try to make my way to the the goal angle so let's see what we can figure out here so I'm going to I'm going to do it in this blue green color anything that I can figure out so this angle is 56 degrees right and let's see these lines are parallel this line here looks like a transversal a transversal so what do we know about well see what's the corresponding angle to this angle right here well it's this angle right now what do we know about corresponding angles for parallel lines when you have a transversal well that's 56 degrees 56 degrees right because corresponding angles are equal we get done a lot of other stuff we could figure it out that this angle is 56 degrees but that probably wouldn't have gotten us closer to our goal we could have you know that angles 56 degrees and it's corresponding angles also 56 degrees that wouldn't have gotten us any closer to our goal we could have figured out that this is 180 minus 56 right which is what 124 degrees that really wouldn't have helped us much but I'm just showing you these are all things that you can do while playing the angle game but anyway the first step I said well these are corresponding angles so that's 56 degrees so let's see I need to figure out this angle right here I know this one and they're in a triangle right you see this triangle if only I knew this angle if only I knew this angle can you figure out this angle well it is supplementary to this 115 degrees right so this green angle Plus this purple angle is equal to 180 so this is 180 minus 115 so what's that 180 minus this is 65 degrees 65 degrees so what have we done so far we just said well these are parallel lines so corresponding angles are equal so this 56 degrees is equal to this 56 degrees and then we said well this green angle and this purple angle are supplementary so they have to add up to 180 so this is 115 then this is 65 which is just 180 minus 115 right and I think you might see where I'm going now now we know two sides two angles of a triangle and if we know two angles of a triangle what can we figure out about the third well we know the angles in a triangle add up to two 180 right so we know let's call this X we know that X plus 56 plus 65 equals 180 right what's 56 plus 65 this is where I always mess up on the addition and the subtraction so 5 plus 6 is 110 hundred this is 121 I believe 121 right can 71 right now determine one equals 180 and then X is equal to let's see 180 minus 20 is 60 so it's 59 X is equal to 59 degrees X is equal to 59 degrees there we go we have accomplished our first goal in the angle game and there you saw it so let's do it let's do a tougher a tougher angle problem this one maybe won't involve parallel lines but I just want to show you everything it really just boils down to everything we learned about parallel lines and and and triangles and angles adding up to each other so this one involves a star let me draw the star so get a line from there there draw a line from there to there draw a line from there to there draw a line from there to there now what do we know about this well we know that this angle is 75 - oh boy I'm using the wrong tool this angle is 75 degrees we also know that this angle is 75 degrees we know this angle here is 101 degrees and your mission in this angle game is to figure out is to figure out this angle right here what is this angle and this is a good time to pause because I will now show you the solution so what can we do here so this angle well geez I just like to just mess around and see what I can figure out so if this angle here is 101 degrees what other angles can we figure out we could figure out well we could figure out this angle we can figure out a bunch of angles we could figure out that this is let me switch to color for these are my figure out angles so that's 101 then this is supplementary that's 79 degrees right that's also 79 degrees right because this is also supplementary this angle right here is opposite to it so this angle right here is going to be 101 degrees 101 degrees what else can we figure out huh we could figure out this angle right because supplementary we can figure out this angle we could also figure out this angle because we see this triangle right here this angle plus 75 plus 75 is it going to equal 180 right so this let's call this angle B B for blue so B plus 75 plus 75 it's going to equal 180 right and I'm just using this this triangle right here so B plus 150 is equal to 180 or B is equal to 30 degrees so we're able to figure this out now what will you do if I told you that we are now ready to figure out this yellow angle and it might not be obvious to you can have to look at the triangle in the right way and the SAT will do this to you all the time all the time that's why I'm testing you this way well let me a little hint look at this triangle I'm using not ideal non-ideal color let me do it in red so it really stands out look at this triangle I'm telling you the hardest thing about these problems is just looking at the right triangle and and kind of seeing that oh wow you know I actually can figure out something look at this triangle right here we know this angle of it 101 degrees we know this angle we just figured it out it was 30 degrees so all we have left just to figure out this yellow angle then call it X right so X plus 101 x plus 101 plus 30 is equal to 180 degrees because the angles in a triangle add up to 180 degrees so X plus 131 is equal to 180 X is equal to what 50s with 49 degrees there you go we've done the second problem in the angle game I think that's all the time I have now in this video in the next video maybe I'll do a couple more of these angle game problems see you soon