Learn about Angle Game - part 2 Video

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Learn about Angle Game - part 2

Welcome back. Let’s do a couple of more angle game problems and hopefully this will make you an angle game expert. Let’s start. I have to start drawing again and let’s say we know the following angle. We know this angle right here is 41-degrees and we know that that this angle here is a 113-degrees. We know this angle here is 101-degrees. What we have to figure out if this is the goal of this angle game. We want to figure out what this angle is. Like always, I encourage you to try it on your own. I'll pause the video and then you just try to work it through. If you get stuck then play the video again and hopefully, I'll have a solution for you. It falls right now but otherwise, let me explain how to do this. Let’s see. We know this; this, and this and we want to figure out this angle. So how could we figure out this angle? What are the possible strategies? Well if we knew this angle here, we could say they are supplementary but that angle seems like a hard angle to figure out too because it is not a part of any triangles. But this angle is a part of this triangle right here so if we were able to figure out this angle and this angle these green angles. If we are 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 give you a hint. But let’s see, 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 all kind of the same line so this is a 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 in the corner of some place so you know we can see if it’s a part of any triangles. Where do you say is part of this triangle but doesn’t help us because we don’t know this angle and that’s actually our goal. What other triangles isn't a part of? What’s the part of this triangle right here? That’s why I like the star problem because it has all these triangles in it. It might not be obvious to you the first time you look at it. But more you look at it is you see all these triangles, so it is a part of this triangle and it is also part of this triangle. I'm going to draw this triangle and I don’t know the color because I think it’ll be clear to you that this is a useful triangle to see that is a part of this triangle. There you go as we have that triangle. 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 thus angle plus 113 plus 41 is going to equal a 180 degrees because with the three angles of the triangle. Let me call this G for green. Since we call this G for green, so we know G plus 113 degrees, 113, that’s this one right here plus 41. Remember where looking at this triangle. That’s the hardest part of just keeping track of which triangle we are looking at. It’s going to equal 180 degrees. G plus what is this? A 154 right 40, 50, or a 154 is equal to 180 degrees. That’s how I always where messed up on the addition and so the G is equal to well just this 26-degrees because I just subtract the 154 from both sides, 26-degrees. We are 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. So our goal, which is just call as X. X plus G which is 26 degrees which we just figured that out. 26 plus this angle is 79 and we figured that out because it was a supplementary to this angle. This is going to equal 180-degrees. So X plus what is this, a 105? It's 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 were all generated on the Khan Academy website dynamically by the computer. Who ever wrote this software must be a genius. But anyway, back to the problems. Let me draw out some more. There is going to be a very straight forward drawing. It’s very much just two triangles next to each other—it goes like that and I think I am done in my drawing. There you go. I am done with my drawing so let’s see. What do we know about this triangle and what do we need to figure out? So if I am going to tell you that this angle here is 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. Our goal and our mission in this round is to figure out what this angle is. And maybe we could do it in a good color. Maybe we can do it in a couple of different ways. One thing we could do is 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 because we know two angles of this triangle, so we could figure that out. Let’s just call this—I must call this Y. So Y plus 122 plus 28-degrees is going to equal 180. So Y plus, this is 150 is equal to 180. So Y is equal to 30 degrees. So this is equal to 30 degrees. This if is 30 degrees and this big angle here is 86 so our goal, let’s call that X. So X is just going to 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 in the other way. Well, we could say instead of doing 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 so it has to add up to a 180. So this plus 122 is 180. So what does that make this? It makes these 58 degrees. This plus this is going to be 180. So if 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 can look at this big triangle here, big triangle here. And we know this side and we could figure out this. This is called as the 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 am doing any of my maths correctly but let’s just hope. Z is equal to 66. 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 or X. So X plus 66 plus 58 is equal to 180. So I already think I might have been on mistake some place in the in the addition so this time around, I get X is equal to 66 plus 58 is a 110 plus 14, so 180 minus 124. So now got it, it equaled to, X is equal to 56-degrees. Great! I actually got the answer. I was looking at this I thought it was 50 but it was 56 right, 86 minus 30. So X is equal to 56-degrees again. So we did two different ways and 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’ve did all my additions and subtractions correctly and you get the exact same answer. Hopefully, you find the angle game fun and you’ll be playing this with your friends. I’ll see you later.

Khan Academy

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http://www.khanacademy.org/

Welcome back. Let’s do a couple of more angle game problems and hopefully this will make you an angle game expert. Let’s start. I have to start drawing again and let’s say we know the following angle. We know this angle right here is 41-degrees and we know that that this angle here is a 113-degrees. We know this angle here is 101-degrees. What we have to figure out if this is the goal of this angle game. We want to figure out what this angle is.

Like always, I encourage you to try it on your own. I'll pause the video and then you just try to work it through. If you get stuck then play the video again and hopefully, I'll have a solution for you. It falls right now but otherwise, let me explain how to do this. Let’s see. We know this; this, and this and we want to figure out this angle. So how could we figure out this angle? What are the possible strategies? Well if we knew this angle here, we could say they are supplementary but that angle seems like a hard angle to figure out too because it is not a part of any triangles.

But this angle is a part of this triangle right here so if we were able to figure out this angle and this angle these green angles. If we are 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 give you a hint. But let’s see, 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 all kind of the same line so this is a 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 in the corner of some place so you know we can see if it’s a part of any triangles. Where do you say is part of this triangle but doesn’t help us because we don’t know this angle and that’s actually our goal. What other triangles isn't a part of? What’s the part of this triangle right here? That’s why I like the star problem because it has all these triangles in it. It might not be obvious to you the first time you look at it. But more you look at it is you see all these triangles, so it is a part of this triangle and it is also part of this triangle. I'm going to draw this triangle and I don’t know the color because I think it’ll be clear to you that this is a useful triangle to see that is a part of this triangle. There you go as we have that triangle.

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 thus angle plus 113 plus 41 is going to equal a 180 degrees because with the three angles of the triangle. Let me call this G for green. Since we call this G for green, so we know G plus 113 degrees, 113, that’s this one right here plus 41. Remember where looking at this triangle. That’s the hardest part of just keeping track of which triangle we are looking at. It’s going to equal 180 degrees.

G plus what is this? A 154 right 40, 50, or a 154 is equal to 180 degrees. That’s how I always where messed up on the addition and so the G is equal to well just this 26-degrees because I just subtract the 154 from both sides, 26-degrees. We are 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.

So our goal, which is just call as X. X plus G which is 26 degrees which we just figured that out. 26 plus this angle is 79 and we figured that out because it was a supplementary to this angle. This is going to equal 180-degrees. So X plus what is this, a 105? It's 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 were all generated on the Khan Academy website dynamically by the computer. Who ever wrote this software must be a genius. But anyway, back to the problems.

Let me draw out some more. There is going to be a very straight forward drawing. It’s very much just two triangles next to each other—it goes like that and I think I am done in my drawing. There you go. I am done with my drawing so let’s see. What do we know about this triangle and what do we need to figure out? So if I am going to tell you that this angle here is 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.

Our goal and our mission in this round is to figure out what this angle is. And maybe we could do it in a good color. Maybe we can do it in a couple of different ways. One thing we could do is 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 because we know two angles of this triangle, so we could figure that out. Let’s just call this—I must call this Y. So Y plus 122 plus 28-degrees is going to equal 180. So Y plus, this is 150 is equal to 180. So Y is equal to 30 degrees.

So this is equal to 30 degrees. This if is 30 degrees and this big angle here is 86 so our goal, let’s call that X. So X is just going to 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 in the other way. Well, we could say instead of doing 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 so it has to add up to a 180. So this plus 122 is 180. So what does that make this? It makes these 58 degrees. This plus this is going to be 180. So if 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 can look at this big triangle here, big triangle here. And we know this side and we could figure out this. This is called as the 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 am doing any of my maths correctly but let’s just hope. Z is equal to 66. 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 or X.

So X plus 66 plus 58 is equal to 180. So I already think I might have been on mistake some place in the in the addition so this time around, I get X is equal to 66 plus 58 is a 110 plus 14, so 180 minus 124. So now got it, it equaled to, X is equal to 56-degrees. Great! I actually got the answer. I was looking at this I thought it was 50 but it was 56 right, 86 minus 30. So X is equal to 56-degrees again.

So we did two different ways and 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’ve did all my additions and subtractions correctly and you get the exact same answer.

Hopefully, you find the angle game fun and you’ll be playing this with your friends. I’ll see you later.

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