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