# Measuring angles in degrees | Angles and intersecting lines | Geometry | Khan Academy

Now that we know

what an angle is, let’s think about how

we can measure them. And we already hinted

at one way to think about the measure of angle in

the last video where we said, look, this angle XYZ seems

more open than angle BAC. So maybe the

measure of angle XYZ should be larger than

the angle of the BAC, and that is exactly

the way we think about the measures of angles. But what I want to

do in this video is come up with an exact

way to measure an angle. So what I’ve drawn over here is

a little bit of a half-circle, and it looks very

similar to a tool that you can buy at your

local school supplies store to measure angles. So this is actually a little bit

of a drawing of a protractor. And what we do in something

like a protractor– you could even construct

one with a piece of paper– is we’ve taken a

half-circle right here, and we’ve divided it

into a 180 sections, and each of these marks

marks 10 of those sections. And what you do

for any given angle is you put one of the

sides of the angle. So each of the rays

of an angle are considered one of its sides. So you put the

vertex of the angle at the center of

this half-circle– or if you’re dealing with

an actual protractor, at the center of

that protractor– and then you put one

side along the 0 mark. So I’m going redraw this

angle right over here at the center of

this protractor. So if we said this is Y, then

the Z goes right over here. And then the other ray, ray

YX in this circumstance, will go roughly

in that direction. And so it is pointing on the

protractor to the– let’s see. This looks like this

is the 70th of section. This is the 80th section. So maybe this is, I would

guess, the 77th section. So this is pointing

to 77 right over here. Assuming that I drew it the

right way right over here, we could say the measure of

angle XYZ– sometimes they’ll just say angle XYZ is equal

to, but this is a little bit more formal– the measure

of angle XYZ is equal to 77. Each of these little sections,

we call them “degrees.” So it’s equal to

77– sometimes it’s written like that, the same

way you would write “degrees” for the temperature outside. So you could write “77 degrees”

like that or you could actually write out the word

right over there. So each of these

sections are degrees, so we’re measuring in degrees. And I want to be clear,

degrees aren’t the only way to measure angles. Really, anything that

measures the openness. So when you go

into trigonometry, you’ll learn that you

can measure angles, not only in degrees,

but also using something called “radians.” But I’ll leave that

to another day. So let’s measure this

other angle, angle BAC. So once again, I’ll

put A at the center, and then AC I’ll put along the 0

degree edge of this half-circle or of this protractor. And then I’ll point

AB in the– well, assuming that I’m drawing

it exactly the way that it’s over there. Normally, instead

of moving the angle, you could actually move the

protractor to the angle. So it looks something

like that, and you could see that it’s pointing to

right about the 30 degree mark. So we could say that

the measure of angle BAC is equal to 30 degrees. And so you can look

just straight up from evaluating these

numbers that 77 degrees is clearly larger than 30

degrees, and so it is a larger angle, which makes sense

because it is a more open angle. And in general, there’s a

couple of interesting angles to think about. If you have a 0 degree

angle, you actually have something that’s

just a closed angled. It really is just a

ray at that point. As you get larger and larger or

as you get more and more open, you eventually get to a

point where one of the rays is completely

straight up and down while the other one

is left to right. So you could imagine

an angle that looks like this where one ray

goes straight up down like that and the other ray goes

straight right and left. Or you could imagine

something like an angle that looks like this where, at least,

the way you’re looking at it, one doesn’t look

straight up down or one does it look

straight right left. But if you rotate it, it would

look just like this thing right over here where one is

going straight up and down and one is going

straight right and left. And you can see from our

measure right over here that that gives us

a 90 degree angle. It’s a very interesting angle. It shows up many, many times

in geometry and trigonometry, and there’s a special word

for a 90 degree angle. It is called a “right angle.” So this right over

here, assuming if you rotate it around,

would look just like this. We would call this

a “right angle.” And there is a notation to

show that it’s a right angle. You draw a little part of

a box right over there, and that tells us that this

is, if you were to rotate it, exactly up and down while

this is going exactly right and left, if

you were to rotate it properly, or vice versa. And then, as you

go even wider, you get wider and wider

and wider and wider until you get all the way to

an angle that looks like this. So you could imagine

an angle where the two rays in that

angle form a line. So let’s say this is

point X. This is point Y, and this is point Z. You

could call this angle ZXY, but it’s really

so open that it’s formed an actual line here. Z, X, and Y are collinear. This is a 180 degree angle where

we see the measure of angle ZXY is 180 degrees. And you can actually

go beyond that. So if you were to go all

the way around the circle so that you would get back

to 360 degrees and then you could keep going around

and around and around, and you’ll start to

see a lot more of that when you enter a

trigonometry class. Now, there’s two

last things that I want to introduce in this video. There are special

words, and I’ll talk about more types of

angles in the next video. But if an angle is

less than 90 degrees, so, for example, both of

these angles that we started our discussion with are

less than 90 degrees, we call them “acute angles.” So this is acute. So that is an acute

angle, and that is an acute angle

right over here. They are less than 90 degrees. What does a non-acute

angle look like? And there’s a word for

it other than non-acute. Well, it would be

more than 90 degrees. So, for example– let

me do this in a color I haven’t used– an angle

that looks like this, and let me draw it a little

bit better than that. An angle it looks like this. So that’s one side of the

angle or one of the rays and then I’ll put the other

one on the baseline right over here. Clearly, this is

larger than 90 degrees. If I were to

approximate, let’s see, that’s 100, 110,

120, almost 130. So let’s call that maybe

a 128-degree angle. We call this an “obtuse angle.” The way I remember it as acute,

it’s kind of “a cute” angle. It’s nice and small. I believe acute in either Latin

or Greek or maybe both means something like “pin” or “sharp.” So that’s one way

to think about it. An acute angle

seems much sharper. Obtuse, I kind of

imagine something that’s kind of

lumbering and large. Or you could think

it’s not acute. It’s not nice and

small and pointy. So that’s one way

to think about it, but this is just

general terminology for different types of angles. Less than 90 degrees,

you have an acute angle. At 90 degrees, you

have a right angle. Larger than 90 degrees,

you have an obtuse angle. And then, if you get all

the way to 180 degrees, your angle actually

forms a line.

FIRST!!!

is his angle really 77 degrees? protractor it

he is just explaning,

so just watch & listen.

I swear that your currently the best teacher on planet Earth. I wish more teachers taught this way because you explain everything from the ground up thoroughly and also give great reasoning behind every conclusion.

i have a 360 protractor.

thx. Now i know math very much!!!

One thing I especially like about your service is that your spending your own free time to help millions of people for free and your your improving society, another thing I liked about your videos is that you can download them instantaneously and watch them on any portable device.

You're teaching skills are incredible! I get everything from the very first when you explain it, my teacher makes things so complicated but you make it so simple! Thank you so much for your time of explaining through each process 😀

I am a 53 year old woman studying to take the GRE. Your lessons have been a godsend. I have literally feared mathematics most of my life. I now actually find geometry interesting and enjoy it. Thank you so much!

Why can't more teachers be like you!!! Thank you for taking the time to do these videos, thanks SOOOOO MUCH.

U got me an A+!

I LUV U!

This guy is great

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I love how you teach it has helped me a lot thx

im a college student and i used to not understand this,you have now opened my eyes,congrats you just earned yourself another subscribe

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Thats "a-cute" angle!! What a cutie. lol

thank you, is easy to understand how to measure the angels .

how i remember it is a cute angle… an obese angle (obtuse)

When you have a angle over 180 you need a circle protractor. I just estimate

Thats what she said

I want to die

sixth grader

a very tiny angle measuring 1 degree is called ?

This person is a great teacher.

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2376, 2377, 2378, 2379, 2380, 2381, 2382, 2383, 2384, 2385, 2386, 2387,

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2616, 2617, 2618, 2619, 2620, 2621, 2622, 2623, 2624, 2625, 2626, 2627,

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2700, 2701, 2702, 2703, 2704, 2705, 2706, 2707, 2708, 2709, 2710, 2711,

2712, 2713, 2714, 2715, 2716, 2717, 2718, 2719, 2720, 2721, 2722, 2723,

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2736, 2737, 2738, 2739, 2740, 2741, 2742, 2743, 2744, 2745, 2746, 2747,

2748, 2749, 2750, 2751, 2752, 2753, 2754, 2755, 2756, 2757, 2758, 2759,

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2988, 2989, 2990, 2991, 2992, 2993, 2994, 2995, 2996, 2997, 2998, 2999,

3000, 3001, 3002, 3003, 3004, 3005, 3006, 3007, 3008, 3009, and finally…. 3010

Numair Younus I agree.

I don't know why I'm watching this

Omg finally i get how to find the angle…ive been seqrching this for years!!

protractor is pronounced – pr-e-tract-or

Nice explanation

I love you thank you for helping me

I love KhanAcademy😊

thanks, Kahn Academy I passed GATE 'cos of you.

My friends teacher has a shirt that says " hey your acute" and it's an acute angel talking to another angel

Love this, thank you. Something I am wondering about –at 0:50 why was it originally determined that a half-circle should be divided into 180 sections, as opposed to say, 100 sections or 200 sections or even 182 sections? Why the specific numbers 180 and by extension 360 (for a whole circle)?

"High School Geometry"

Keel me Know

…Augly angles??

Teachers should be ashamed how they cannot teach stuff like this

Sir it's the best mathematics class I have ever had. I I were in mumbai I would have come to you directly for your class. I wish if my school teacher's were like you

I only know a little about Trig. I guess you can use sin, cos, and tan (I guess?) to measure the angle. That way, it is more precise (not talking about accuracy here, that's a different thing.)

OK so maybe someone here can explain to me why do they call it the Xbox 360???

Nice

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