Angle Game (part 2) More examples of the Angle Game.
Angle Game (part 2)
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- 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?
- 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.
- And these problems are all generated on the
- Khan Academy website, dynamically by the computer.
- Whoever wrote this software must be a genius.
- But anyway, back to the problems.
- 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.
- 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.
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