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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.