WEBVTT

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So let's review everything that
we know so far, because it's

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good to keep reviewing.

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Because these are things
you should never forget

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the rest of your life.

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So if I have a line and if I
draw an angle that goes--

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let's say this is the
pivot point, right?

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If I go all the way around
the line, or in a circle,

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that's 360 degrees.

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11
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We learned that there are
360 degrees in a circle.

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Right?

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We also learned that if
I have lines like this.

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If I have two angles-- let
me draw it like that.

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16
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And this is angle x.

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This is angle y.

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x and y are supplementary.

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And that just means that
they add up to 180 degrees.

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x plus y is equal
to 180 degrees.

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And why does that make sense?

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Because look, if we add
up x plus y we have gone

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halfway around the circle.

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So that's 180 degrees, right?

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So hopefully we
have learned that.

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And then let me switch colors
for the sake of variety.

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Let me use my line tool.

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If I have-- let's see,
I'm going to draw

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perpendicular lines.

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If I have that line, and
then I have that line.

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And they are perpendicular.

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And then I have another line.

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Let's say it goes like that.

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39
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And then I say that
this is angle x.

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Woops.

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This is angle x.

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And this is angle y.

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44
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Well, I said this line and this
line are perpendicular, right?

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So that means that they
intersect at a 90 degree angle.

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So we know that this whole
thing is 90 degrees.

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And so what do we
know about x plus y?

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Well, x plus y is going
to equal 90 degrees.

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51
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Or we could say that x
and y are complementary.

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And I always get confused
between supplementary

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and complementary.

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You just got to memorize it.

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I don't know if there's
any-- let's see, is

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there any easy way?

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180, supplementary.

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You could say that 180-- 100
starts with an O, which

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supplementary does
not start with.

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So there.

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There's your mnemonic.

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Complementary.

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And 90 starts with an N,
and complementary does

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not start with an N.

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That's your other mnemonic.

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Complementary.

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I don't know if I'm
spelling it right.

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Who cares?

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Let's move on.

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So let's learn some more
stuff about angles.

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And what I'm going to do is I'm
going to give you an arsenal,

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and then once you have that
arsenal you can just tackle

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these beastly problems that
I'm going to throw at you.

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So just take these for granted
right now, and then in a few

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videos, probably, we're
going to tackle some

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beastly problems.

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And you know, I'm
using variables here.

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And if you're not familiar
with variables you

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can put numbers here.

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If x was 30 degrees, then y
is going to be 60 degrees.

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Right?

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Or in this case, if x is, I
don't know, 45 degrees, then y

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is going to be 135 degrees.

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That other way.

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Let me draw another property of
angles of intersecting lines.

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So if I have two angles, two
lines that intersect like this.

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90
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So a couple of
interesting things.

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So first, I'm going to teach
you about opposite angles.

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Let me switch colors.

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Let me switch to yellow.

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So if this is x degrees, then
it turns out that the angle

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opposite to it is also
equal to x degrees.

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98
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And you don't believe me?

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Well let me prove it to you.

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Let's say we call this,
I don't know, let's

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call this y degrees.

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Right?

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And I'm going to prove
to you that the x and

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the y are the same.

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Well what do we know already?

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Let's call this other angle--
and I'm doing this to

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confuse you-- angle z.

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Well what do we know about
angle x and angle z?

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It may not be obvious to you
because I've drawn it slightly

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different, but I'll give you
a small hint with

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an appropriately
interesting color.

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So what angle is this
whole thing right here?

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Well I'm just going
along a line, right?

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That's halfway around a circle.

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So what does x plus z equal?

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Well, x plus z is going to
equal that larger angle.

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x plus purple z is going to
equal-- I think I'll switch to

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the blue; maybe it's taking too
much time for me to switch--

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is equal to 180 degrees.

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Or x and z are supplementary.

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I've run out of space.

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So what do we know about z?

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Well z is equal to 180 minus x.

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Right?

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Because x plus z is 180.

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Fine.

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Now, what's the relationship
between z and y?

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Well, z and y are
also supplementary.

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Because look, if I
drew this angle here.

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Look at this big angle.

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135
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What angle is that?

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Well once again I'm still going
halfway around the circle.

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Right?

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But now I'm using this
line right here.

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So that's 180 degrees.

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So we know that angle z
plus angle y is also

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equal to 180 degrees.

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Right?

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Or, I don't want to keep
writing it, but z and y

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are also supplementary.

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But we just figured out
that z is 180 minus x.

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Right?

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So let's just substitute
that back in here.

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So we get 180 minus x plus
y is equal to 180 degrees.

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Why don't we subtract 180
degrees from both sides

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of this equation.

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That cancels out, and we get
minus x plus y is equal to 0.

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And then add x to both sides
of this equation, and

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we get y is equal to x.

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So x is equal to y.

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And if you've played around
with this, if you just drew a

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bunch of straight lines and
they intersected at different

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angles, I think when you
eyeball it it would make sense.

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And then similarly, if that's z
then the other opposite angle

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here is also z degrees.

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So what do we know now?

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The total angles in a
circle, 360 degrees.

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When two angles kind of
combine, go halfway around the

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circle-- or they combine,
kind of form a line.

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There's different ways
you can think about it.

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We know they're supplementary.

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They add up to 180 degrees.

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x plus y is 180 degrees.

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If they add up to 90
it's complementary.

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x plus y is 90.

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And then opposite angles
are equal to each other.

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Right?

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This angle is equal
to this angle.

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And then this angle is going to
be equal to this angle for the

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same reason-- because
it's opposite.

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In the next video I'm going
to show you about parallel

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lines and transversals.

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More fancy words for what
I think are fairly

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straightforward concepts.

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I'll see you in the next video.