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## Geometry (all content)

# The angle game

Using what we know to solve for angles in the Angle Game. Created by Sal Khan.

## Video transcript

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