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