Tip:
Highlight text to annotate it
X
>> This is YourMathGal,
Julie Harland.
Please visit my website
at yourmathgal.com,
where all of my videos were
organized by topic.
This is part 1
of Degree Measures of Angles
and you should already be
familiar with basic
terminology for angles.
In this video, we're going
to define the degree measure
of an angle as the meaning
of these four different types
of angles, acute angle,
obtuse angle, right angle,
and straight angle.
So, the most common unit
for measuring angles is
the degree.
Most people heard of degrees
when they're measuring angles.
There are other ways
of measuring angles.
That degree is certainly the
first that most people hear
about and this was discovered
around 2000 BCE.
I don't know, plus or minus,
probably, a few hundred years.
I don't know exactly
when it was.
But they signed 360 degrees
to a complete rotation
of a ray.
So, this is how we write
degrees, this little symbol
right here.
So if you want 360 degrees,
you write 360
and you put this little symbol
up here that means degrees.
So if you look at this angle
in standard form here,
here's the initial side.
And then if we rotate,
we go all the way around
and back to where we start.
That's a full rotation
and we call
that a full 360
degree rotation.
So we say this angle here
that you see,
it's kind of funny,
it's a full rotation,
you can have an angle
like that, it's 360 degrees.
You might have heard
of somebody referring
to somebody doing a jump-off,
a diving board, as doing a 360
and that would been
like a full revolution before
they dive in, et cetera.
So if a complete revolution is
360 degrees,
then half of a full revolution
would be what?
Well, we do have half
of 360 degrees
which is 180 degrees.
So let's see what
that looks like.
That would be half
of a revolution.
So let's see.
Let's say here is our angle
and here's
where it ends, okay?
So, right here is the middle
part of it.
And from here to here,
that would be 180 degrees.
So how many degrees is 1/4
of a full revolution?
What do you think
that would be?
Well, we'd have 1/4
of a full revolution.
Full revolution is 360
and so 1/4
of that would be 90 degrees.
So what does that look like?
What's a 90-degree angle
look like?
And my guess is you've
probably seen that before.
So 1/4 of a revolution would
be, you start here
at the X axis
and you go only fourth other
way around
and so then this would be 90
degrees, this angle you see
right here.
Now, it's common
for a 90-degree angle
to be written--
see, like this.
[ Silence ]
So let's say we want
to do this one.
We can. Often, do you note
that it's 90 degrees?
They put a little square here.
What this is saying is sort
of squared of.
Ninety degrees is the angle
and all four angles
in the square have 90 degrees.
So you'll see this little box
denote a 90-degree angle,
okay?
So that's another way
of writing a 90-degree angle.
That's the notation that's
often used as oppose
to this little arrow,
all right?
But in any case,
we've got that 1/4
of a revolution would be
90 degrees.
And this angle is called--
90 degrees is called a
right angle.
Okay? Okay.
So how many degrees is 1/6
of a full revolution?
And then try drawing
when in standard position.
So what would that be?
One sixth of a full revolution
would be 1/6 of 360 degrees
which is 60 degrees.
Hopefully, you're okay
with this.
I'm just reducing 6 goes
in the 360, 60.
Now what would that look like?
So it's 1/6
of a full revolution.
Here's the way I think of it.
Well, from here to here,
right, all the way over here,
that's 180 degrees
that is half a revolution.
And now I want 60 degrees,
that's 1/3 of that.
So I think of this as 1/3
of the 180 degrees.
That's how I think of it.
So if I think from here
to here is 180 then I have
to think about of a third.
So imagine if you broke it
up into thirds, can you see?
There's an angle,
there's an angle,
there's an angle.
So, each of those would be
about 60 degrees.
Now, I'm just free-handing it,
that's not exactly 60 degrees.
But I'm giving you a basic
look as how I would come
up with something like this.
Right. That's one way
of doing it.
Other people think of it
as well as this
from the right angle is
from here to here is 90
degrees then they break this
up into thirds, 30,
30 and 30 more
and that's how they might come
up about that far is
60 degrees.
So in any case,
your 60 degrees should look
something like this,
about that far up.
So that would be the angle.
Now, you don't usually also
draw it down here
but you could.
So, usually, you just see
where it starts on the axis.
You don't have to draw
that part,
but you show the terminal side
of the angle.
Now, this angle I drew here,
60 degrees,
notice it's the way
when you first learned
about angles, how you think
of an angle.
You don't think
of these full
revolution-type ones.
It's an angle between 0
and 90 degrees, right,
60 degrees.
And an angle between 0
and 90 degrees is called an
acute angle.
So an angle between 0 degrees
and 90 degrees is called an
acute angle.
I didn't really talk
about 0 degrees.
That would mean just here
on the X axis, it doesn't move
at all, all right?
So 0 degrees is just right
here, it doesn't move.
Its terminal
and its initial sides are
exactly the same place.
It doesn't move anywhere.
You won't see an arrow
at all, okay?
So, I hadn't really explicitly
talked about that.
So we've got an acute angle.
We found out like an angle
that goes up 90 degrees,
that's called a right angle.
So we have a right angle
and acute angle.
Let's move
on to the next kind,
special type of angle.
All right.
So how can I draw an angle
that is 135 degrees?
So let's just keep
in mind what we have come
up with so far.
We found out that if I went,
you know, up to here,
you know, in other words,
from there to there,
that was 90 degrees.
And I want to get 135 degrees.
So I've got to go more
than 90 degrees.
And how much more do I have
to go?
Well, 135 degrees minus 90
degrees, I've got 45 degrees
more to go.
And 45 degrees is, well,
that's half of 90.
So I've got half
of this way more to go.
So if I keep going a little
bit further to here,
that would be an estimate
of where 135 degrees is.
So let's see.
So my 35 degree--
135 degree-angle would be kind
of going through the
center here.
So that's what an angle
of 135 degrees goes to.
And so, you know,
you could estimate
where a lot of, you know,
angles are by doing that kind
of reasoning.
Now, this angle here is kind
of big.
It's not between 0 and 90.
It's bigger than 90 degrees.
It still kind of looks
like an angle,
so I don't pout it.
You know, if I just take it
outside and--
look, it still looks
like an angle.
It doesn't look that funny
like the ones
that go all the way around,
right?
And we call an angle
between 90
and 180 degrees an
obtuse angle.
So an angle between 90 degrees
and 180 degrees is called an
obtuse angle.
So you've got an obtuse angle.
We talked about an
acute angle.
We talked about a right angle.
Now, the first angle we looked
at was 180 degrees.
Let's look back at that.
So here was our 180-degree
angle that was half
of a full revolution
and we called this a
straight angle.
An angle that is 180 degrees
is simply called a straight
angle because it just looks
like a straight line.
Now, we could use capital
letters for the angles A, B,
C, D, E, but it's also common
to use some Greek letters.
These are some common ones,
theta, alpha and beta,
and so I'm using those
in this little picture here.
So here's an example
of an acute angle theta,
it's small between 0 degrees
and 90 degrees.
The right angle is exactly 90
degrees, that's alpha here.
An obtuse angle is pretty big
angle but not all the way
to 180 degrees, so it's bigger
than 90, right?
It's wide open but it's less
than 80 degrees,
that's an obtuse angle.
And a straight angle,
the one we just talked
about is when it makes a
straight line,
it's exactly 180 degrees.
This is YourMathGal,
Julie Harland.
Please visit my website
at yourmathgal.com,
where all of my videos were
organized by topic.