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Course: Geometry (all content)>Unit 2

Lesson 8: Sal's old angle videos

The angle game (part 2)

More examples of the Angle Game. Created by Sal Khan.

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• Who knows ALL the angles in the second problem?
(32 votes)
• The straight line was formed from 122 and 58
(1 vote)
• At , Sal said X=50' but probably meant X=56'.
(6 votes)
• he fixed it around there is a little note that pops up
(2 votes)
• Is 0/0 undefined?
(3 votes)
• In a fraction, if the zero is at the denominator and the numerator holds a real number or to make it simple any number except zero then,the division is possible and the quotient or your answer will become zero. E.g. 0/4=0.This division terminates after finding the answer.Well if we were to divide zero by zero then we would have to divide the each zero which comes as an answer by zero again.E.g. 0/0 = 0. this answer "0" is to be again divided by zero to find the answer again as the division is left incomplete. so again 0/0 = 0. So if you go on dividing zero by zero,the answer will always come zero.Even if we try this division a million times,the answer is always going to be 0.Hence,0/0 is undefined.
(1 vote)
• If we look clearly, a star is a figure which has a pentagon(a five-sided fig.) in the middle.And the sides of this pentagon form a base for 5 different triangles on each side of this pentagon.Well,my doubt regarding these triangles is are these triangles isosceles? or are they scalene?Please someone clarify my doubt.
(3 votes)
• Unless stated, there is no reason to think they'd be isosceles. so your doubt is correct. Sal shows that the lower-left triangle is not isosceles at when he shows that none of the triangle's angles equal the other. If it was isosceles, two of the angles would be the same.
(2 votes)
• why is it called a game but it is a video
(3 votes)
• I don't know about you guys, but that 86 degree angle on the second shape just doesn't look like 86 degrees
(2 votes)
• Not all angles are drawn to scale. if you see a 90 degree angle, but there is no info on the page that explicitly tells you it is a right angle, it is not a right angle.
(2 votes)
• why is the video not working
(2 votes)
• So, a star could basically be 8 smaller triangles?
(2 votes)
• what about a parrallel line with 2 transvarsals how would u solve for all tha angles i am in 8th grade
(1 vote)
• The same way! Any parallel set cut by a transversal, two , or even three would still follow the AEA, AIA, Supplementary/ Complimentary angle, etc proof!
(2 votes)
• "I already think I might have made a mistake some place in the addition." You think? Already? Yes Sal, X is 56. Heureka! I thought I would watch through the video and see if you pick that up. =) And you did Sal!

You know guys, if the great Sal can make mistakes so can everyone else! He did admit though that he sometimes makes mistakes in the addition before he actually made the mistake. So it's kind of interesting, as if his subconscious was doing what he was saying.

Personally I think making mistakes is part of the learning process so it's good he made the mistake and even better that he saw it and corrected it. I too often make mistakes just like this one, and I miss the extra points on tests. This shows why you always have to go over your results and see if it's feasible.
(1 vote)
• Thoughtful commentary, Samir. Let's never stop making mistakes!
(2 votes)

Video transcript

Welcome back. Let's do a couple more angle game problems, 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. We know this angle here is 113 degrees. We know this angle here is 101 degrees. And what we have 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 just try to work it through. If you get stuck, then play the video again 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, and we're going to figure out this angle. So how can we figure out this angle? What are the possible strategies? Well, if we knew this angle here, we could say they're supplementary. But 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 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 pause because I just gave you a hint. This green angle, well 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? So 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 we could see if it's part of any triangles. But 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? Well, it'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 the more you look at you see all these triangles. So it's part of this triangle, and it's also part of this triangle. I'm going to draw this triangle another color because I think it'll be clear to you that this is a useful triangle to see that's it's a part of. 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 of the three angles of a triangle. So let me call this, I don't know, g for green. Let's call this g for green. So we know g plus 113 degrees, that's this one right here, plus 41 -- remember, we're looking at this triangle; that's the hardest part just keeping track of which triangle we're looking at -- is going to equal 180 degrees. g plus, what is this, 154? Right? 40, 50, 154 equals 180 degrees. That's always where I mess up on the addition. And so g is equal to, what is this, 26 degrees, right, because I just subtract 154 from both sides. 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, this small one right here. This small triangle. So our goal, which is let's call this x. x plus g, which is 26 degrees -- we just figured that out. 26 plus this angle, 79 -- and we figured that out because it was supplementary to this angle -- is going to equal 180 degrees. So x plus, what is this, 105 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. These problems are all generated on the [? Card ?] Academy website dynamically by the computer. Whoever wrote this software must be a genius. But anyway, back to the problem. Let me draw some more. So this is going to be a pretty straightforward drawing. It's pretty much just two triangles next to each other. Like that and then let me draw another line that goes like that, and then we draw a line that goes like that, and I think I have done my drawing. There you go. I'm have done my drawing. So let's see. What do we know about this triangle and what do we need to figure out? I'm going to tell you that this angle here, this big angle here, is 86 degrees. We also know that this angle here is 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 can 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 this angle is, so we could just subtract this green angle from 86 and we would get our answer. Well, this angle's easy, right, because we know two angles of this triangle, so we could figure that out. Let's just call this, I don't know, let's call this y. So y plus 122 plus 28 degrees is going to equal 180. So y plus 150 is equal to 180. So y is equal to 30 degrees, right? So this is equal to 30 degrees. So this is 30 degrees, and this big angle here is 86. So our goal, let's call that x, so x is going to just be equal to the big angle, 86 minus this angle we just figured out, minus 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 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 58 degrees, right? This plus this is going to be 180. So we figured out this. If we could figure out this, then we could use this triangle. How do we figure out this angle? Well, we could look at this big triangle here, and we know this side, right, and 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 any of my math correctly, but let's just hope. z equals 66. 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. I already think I might have made a mistake some place in the addition. So this time around I get x is equal to -- let's see, 66 plus 58 is 110 plus 14. So 180 minus 124. So now I got it, x 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 it two different ways. That's what I wanted to show you. There's actually not a right answer, as long as you kind of get there eventually. We solved it two different ways and I did all my addition and subtraction correctly, and you get the exact same answer. So hopefully you find the angle game fun and you'll be playing this with your friends. I'll see you later.