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## Geometry (all content)

### Course: Geometry (all content) > Unit 2

Lesson 1: Angle introduction# Angles: introduction

CCSS.Math:

Two rays that share the same endpoint form an angle. Learn about angles and the parts of an angle, like the vertex. Created by Sal Khan.

## Want to join the conversation?

- How are Angles used in everyday life?(721 votes)
- Angles are used to design the most basic and the most complex of polygons (shapes). If you look at your clothing, there are many different angles that are used to design skirts and dresses. Look at the collars of your shirts. Diverse angles used in any sort of art design draws the eye. How about stained glass windows?(74 votes)

- how many angles can you think of?(154 votes)
- Besides the 4 types of angles tabron517 mentioned, there are also full and reflex angles. A full angle is a full 360 degrees and a reflex angle is between 180 degrees and 360 degrees. A full angle looks like this: https://upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Full_angle.svg/380px-Full_angle.svg.png An obtuse angle is between 90 and 180 degrees and a straight angle is 180 degrees.

Hopefully you know the rest: acute --> less than 90, right ---> 90. In between, there's an infinite number of possible angles within the possible degrees an angle can have (you can have a 40.34 degree angle for example). If you actually draw angles out you'll find that you can really define an angle to be at either side of a vertex (the point where the two rays meet) and what you would probably consider the "other side" would usually be a reflex angle, which would look something like this: http://www.mathsisfun.com/images/reflexangles.gif(148 votes)

- Is a vertex the meeting point between two rays or two line segments or two lines, or does it not matter?(92 votes)
- Well, if you look at a angle, it has no arrows, but is still is a ray, and still goes on forever, the angle just doesn't have the arrows. I believe that angle are all rays, but I am not sure. It would be good question to google. Hope this was helpful to you!(64 votes)

- At2:23, Sal says you can't call that angle A, then demonstrates another diagram. I know on the 2nd diagram that you can't call it H, but couldn't you call it A in the first one?(12 votes)
- Even Though it is an angle all by itself, the rule still applies.(14 votes)

- how do you tell a 360° angle from a 720° angle or a 45° angle from a 405° angle?(15 votes)
- At0:03, Sal says that the point is called AB. Can you call it ray BA?(12 votes)
- Yes! It always stays the same, even if you do switch it from AB to BA.(4 votes)

- say that i wanted to name the angle BAC but i wanted name the reflex angle, how would i do it?(6 votes)
- you subtract 360 by the inside angel(12 votes)

- why a right angle is ninety degrees?(8 votes)
- Each full circle is 360 degrees. A quarter of that would be a right angle, or 90 degrees.(5 votes)

- And pretend this isn't a greater than sign, but is this an angle? >(7 votes)
- Typically, we use the less than sign < to represent an angle. You can tell the difference between an angle and less than sign because angles will be indicated with letters (ex. <A).(6 votes)

- What is an angle? We jump directly into line arrays and segments and where angles are found but we have no clue of what an angle is at it's most basic explanation.(6 votes)
- An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.(5 votes)

## Video transcript

Let's say we have one ray over
here that starts at point A and then goes through
point B. And so we could call this
ray-- let me draw that a little bit straighter--
we could call this ray AB. Ray AB starts at A,
or has a vertex at A. And let's say that
there's also a ray AC. So let's say that C is
sitting right over there. And then I can draw another
ray that goes through C. So this is ray AC. And what's interesting
about these two rays is that they have the
exact same vertex. They have the exact
same vertex at A. And in general,
what we have when we have two rays that have
the exact same vertex, you have an angle. And you're probably
already reasonably familiar with the concept
of an angle, which I believe comes from the Latin
for corner, which makes sense. This looks like a
little bit of a corner right over here that
we see at point A. But the geometric
definition, or the one that you're most
likely to see, is when two rays share
a common vertex. And that common
vertex is actually called the vertex of the angle. So A is the vertex. Not only is it the vertex of
each of these rays, ray AB and ray AC, it is also
the vertex of the angle. So the next thing I
want to think about is how do we label an angle. You might be tempted to
just label it angle A. But I'll show you in a
second why that's not going to be so clear
to someone, based on where our angle
is actually sitting. So the way that you
specify an angle-- and hopefully this will
make sense in a second-- is that you say angle-- this
is the symbol for angle, and it actually looks
strangely similar to this angle right over here. But this little
pointy thing, or it almost looks like
a less-than sign. But it's not quite. It's flat on the
bottom right over here. This is the symbol for angle. You'd say angle BAC. Or you could say angle CAB. In either case, they're kind
of specifying this corner. Or sometimes you could
view it as this opening right over here. And the important
thing to realize is that you have the vertex
in the middle of the letters. Now you might be
saying, wait, why go through the trouble
of listing all three of these letters. Why can't I just
call this angle A? And to see that, let me
show you another diagram. And although the geometric
definition of an angle involves two rays that have
the same vertex, in practice, you're going to see
many angles that are made up of lines
and line segments. And you could imagine that
you could continue those line segments on and on
in one direction. And then they would become rays. So in that way,
they're consistent with this definition. But let's say I have one line
segment that looks like that. Let me label some points here. So we've already used ABC. So I'm going to
call this D and E, points D and E. So this
is line segment DE. And let's say I also
have a line segment FG. And let's say this point
where these two line segments intersect, let's
call that point point H. Now how could we specify this
angle right over here? Can we just call that angle H? Well, no. Because if we just said angle H,
the angle that has a vertex H, it could be this
angle right over here. Or it could be this
angle right over here. Let me draw it this way. You could view it that way. Or it could be that
angle over there. It could be this
angle over here. It could be this
angle over here. Or it could be that
angle over there. And so the only way
to really specify which angle you're talking about
well, is to give three letters. So if you really did want
to talk about that angle right over there, you
would call that angle EHG. So that is angle EHG. Or you could actually
call that angle GHE. If you wanted to specify
this angle right over here, the one made up of, if you
imagine that ray and that ray, if you were to keep on
going past those points, then you could call that
angle DHG, or angle GHD. I think you get the point. This angle up here
could be FHD or EHF. And this one could
be FHD or DHF. And when you do
it this way, it's very clear what angle
you are referring to. So now that we have a general
idea of what an angle is, and kind of how do we
denote it with symbols, the next thing you
might be curious about is, it doesn't look like all
angles are kind of the same. It seems like some
angles open up or are more open than others. And some are a little bit
more closed in than others. And that actually is the case. So for example, let's
take two angles here. So let's say I have one
angle that looks like that. So I'll started reusing letters. So let's say that this is A, B
and C. I could make these rays. I could keep on going and
make them rays if I like. Or I could just keep
them as line segments. So right over here,
I have angle BAC. And let's say over
here, I have angle-- so let me draw another one-- and
let's say this is angle XYZ. And once again, I
could draw them as rays if I like, to go
on and on and on. So it's angle XY and Z. And so when you
just look at these, you just eyeball
these two angles, it looks like this
one is more open. So this one looks more open. While this one over here looks
more closed, at least relative to this one. So maybe when we
measure angles, we should measure it based on
how open or closed they are. And that actually is the case. And so without even telling
you how we measure an angle, you could say that the measure
of angle XYZ, the measure of this angle, is greater
than the measure of this angle right over here. And any convention we use for
measuring angles is essentially going to be a measure
of how open or how closed an angle actually is. And I'll take that
up in the next video where we'll see how to
actually measure an angle.