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## Geometry (all content)

# Intro to angles (old)

What an angle is. Angles in a circle. Complementary and supplementary angles. Created by Sal Khan.

## Video transcript

Hello. In this series of presentations
I'm going to try to teach you everything you need to know
about triangles and angles and parallel lines. And this is probably the
highest yield information that you could ever learn, and
especially in terms of standardized tests. And then when we've learned all
the rules we'll play something that I call the angle game,
which is essentially what the SAT makes you do over
and over again. So let's start
with some basics. Well, you know
what an angle is. Well actually, maybe you
don't know what an angle is. And I'll tell you
what an angle is. If I have two lines-- I'm
going to draw a thicker line than that. If I have two lines and they
intersect at some point, the angle is a measure of exactly
kind of how wide the intersection is between
those two lines. Let me use a better tool. So this is the angle. An angle is how wide those
two lines kind of open up. And they're measured either in
degrees or radians, and for the sake of most of a geometry
class we'll use degrees. And when we start doing
trigonometry you'll learn radians. Or maybe you could
learn it now. And you're probably
familiar with this. 0 degrees would be these two
lines on top of each other. This, if I were to just eyeball
it, looks like 45 degrees. If I had the lines even
wider apart like that, that's 90 degrees. And 90 degree lines are also
called perpendicular, because they are-- I feel like saying,
because they are perpendicular-- but because one
is going completely vertical while the other is
going horizontal. It's actually amazingly
difficult to find the exact right wording. But I think you get the idea. By definition, perpendicular
lines have a 90 degree apart from each other. And, you know, you've seen this
all the time in things like squares and rectangles. If I were to draw a
rectangle like that. Right? A rectangle is made up of a
bunch of perpendicular lines, or lines at 90 degree angles. So example. These two lines are at
a 90 degree angle. The way you draw a 90
degree angle is you draw a little box like that. That's the same thing as
doing this-- as doing a 90 degree angle. And you could even
get wider angles. So if you go above 90 degrees. So let's say I had
lines like this. So this would be-- I don't
know, I'm just eyeballing it-- 135 degrees or
something like that. If you ever want to really
measure the angles, you can use something called a protractor. That's a tool maybe your
teachers can help you use that. So that'd be 135 degrees. And then if you had it so wide
that the two lines are actually almost forming a line, then
this becomes 180 degrees. It's almost like one line. Right? This is 180 degrees. And then you can keep going. So if this angle here is 135
degrees, you can actually also measure this angle right here. Let me do it in a different
color just to add some variety. So then this angle right here. So the angles in a circle
are there are 360 degrees in a circle. So if this is 135, this magenta
angle would be 360 degrees minus 135 degrees. And that's equal to what? That's 225 degrees, is
this magenta angle. And then we could do
other things like that. So one, you know that the
degrees in the circle are 360 degrees. This is important to know. Degrees in a circle
are 360 degrees. It's also important to know
that if you just go kind of halfway around a circle,
like we did here, that's 180 degrees. Like if you viewed the
pivot point as like, let's say, right here. I mean it looks like just
one line and it really is. But that's 180 degrees. And then if you go quarter
way around the circle, that's 90 degrees. All right? Hopefully you're getting
a bit of an intuition for what an angle is. So now I will teach you
a bunch of very useful rules for angles. Clear this. So let me redraw. So if I had a line like this. I like using the colors, just
so I think it keeps you from getting completely bored. And it might not be completely
intuitive what I'm doing, but let's add an angle like that. And so, let's just say-- you
know, I'm not measuring these exactly-- let's say that
this is 30 degrees. We know that if we go all the
way around the circle, we know that that's 360 degrees. Right? And that's a very ugly
looking around the circle angle that I drew. So then we also know
that this angle right here is 330 degrees. Right? Because this angle plus this
magenta angle is going to equal the whole circle. So this is equal
to 330 degrees. So remember that. The angles in a circle--
or there are 360 degrees in a circle. I don't know if you remember. You probably don't. This was probably
before you were born. But there used to be a game
called 720, and it was a skateboarding game--
it was a video game. And the 720 was essentially
you were trying to jump your skateboard and
spin around twice. And that's 720 degrees. If you go around a circle
twice that's 720 degrees. If you just jump and
spin around once, you went 360 degrees. So you've probably heard this
in just popular culture. But anyway. So 360 degrees in a circle. And you could imagine half
a circle is 180 degrees. So the other important thing to
realize is, like we said, if we go halfway around the
circle it's 180 degrees. But if we have two angles that
add up to that-- so let's say. I don't know if these lines are
thick enough for you to see. Let me draw something thicker. It doesn't look ideal,
but you get the idea. So if we have this
angle, let's call it x. And then this angle is y. What do we know about the
relationship between x and y? Well, we know that the entire
angle is half of a circle. Right? So that's 180 degrees. That's 180 degrees,
this entire angle. So what are angles x and
y going to add up to? I'm trying to stay
color consistent. x plus y are going to
equal-- I'm color blind, I think-- 180 degrees. Or you could write y is
equal to 180 minus x. Or x is equal to 180 minus y. But if x plus y are equal to
180 degrees-- and you can see that it makes sense that they
do-- if you add the two angles you go halfway around a circle. Then that tells us that x and y
are-- and this is a fancy word, and it's just good to commit
this to memory-- they are supplementary angles. That's when you add
to 180 degrees. Now what if we had
this situation. Oh my God, that was horrible. Undo. Let's say I had this situation. Let's see. I draw two perpendicular lines. Right? So this is going a quarter
way around the circle. All right. Let's say this entire angle
here-- I'm drawing it really big-- that's 90 degrees. Right? They're perpendicular. And now if I had two
angles within that. So now if I have two angles
here-- so let's say that this is x and this is y-- what
do x and y add up to? Well, x plus y is 90. And we can say that x and
y are complementary. And it's important to not get
confused between the two. Just remember complementary
means two angles add up to 90 degrees, supplementary means
that two angles add up to 180 degrees. I'm running out of time, so I
will see you in the next video.