Sum of interior angles of a polygon | Angles and intersecting lines | Geometry | Khan Academy

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Showing a generalized way to find the sum of the interior angles of any polygon
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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.
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[@mariahspalace3782]

When he started writing the second shape- I was like, no, why can't we just keep it simple. A+B+C=180. Boom. Done.

[@jreivynz]

Haha 69 likes.

[@laurenmenzies5397]

Math is never simple, there is always a catch

[@Jenny-tu9fc]

this was amazing!! why can't my math teacher teach like this 😭

[@cinnamoroll1981]

yup sooooo true

[@zoranencharity3854]

Yup I wish

[@Rainjustine.]

Same

[@aprammus9580]

Would be awesome

[@shilpakotha481]

Yoo

[@kylemichael110]

If u want to get how many is the triangle in a polygon fast just count the side of a polygon and -2 of what is the side and the answer is the triangle :)

[@sultanalshamsi7629]

Jjöøśšhh or use (n-2)180=x N=number of sides X=interior angle sum

[@----m]

@@sultanalshamsi7629 THANK YOU

[@agentgfxandgames6540]

you are so cute

[@ClemoTekkerz]

I have an assessment on this in school tomorrow and I didn't really understand the way our teacher explained it so this video is really helpful, thanks!

[@luvragerwill]

Same

[@aboodalnama9816]

same

[@noori8801]

been 4 years since that assessment

[@gamercat166]

How’d it go?

[@RichGuy1]

102 where did it come from ??!

[@jesuisbobbyy]

For those who don't understand at minute 8:00 why he writes 2 + (s - 4) when 2 are triangles and 4 are sides is because you can build the first 2 triangles with 4 sides, the remaining triangles are made after every single remaining side. Indeed after the first 2 triangles you can made as many triangles as the remaining sides, that are S - 4 (the 4 initial sides used to build the first 2 triangles).

[@joeytierney7455]

As a middle school math teacher, i love your videos and use them all the time! But you should remove this video and make a fresh one cause your polygon with that crazy side that you redid numerous times over became very hard to follow.

[@luciusirving5926]

This is Euclidean geometry, no wonder it's hard to follow. This is the kind of stuff one would learn in high school and I'm more or less of an algebra expert, so I would understand.

[@trx3640]

@@luciusirving5926 what are you even talking about

[@GlowtreeMC]

Thanks man! 8th grade Geometry student here, this video helps wonders! Gotta go take my test *fingers crossed*

[@miiiiiiraaa]

GlowTree omg that’s 7 years ago !!

[@catsrepic8813]

@@miiiiiiraaa omg that’s 4 months ago!!

[@vontae393]

@@catsrepic8813 OMG ITS BEEN 2 MONTHS AGO

[@Sienna850]

How’s life now? This was 8 years ago

[@luviesni-ki5696]

your 21 now

[@itsclarencetong]

Please never stop making maths videos, I just subscribed!

[@asemaldaras6687]

your now a dad ...

[@NoahMine1]

Bro it’s 7 years

[@mariasullivan493]

Daily Fortnite Battle Royal Clips lmao “ur now a dad” no doubt you’re just watching this cause you were quarantined early and are salty, Fortnite kid.

[@sma530v8]

ok

[@1Tara]

@@NoahMine1 8 now

[@brookethompson7115]

For anyone who is confused you can use this formula: (number of sides - 2)×180= the sum of the interior angles of a polygon

[@jisooteddykim]

Thanks bro

[@HaiderPlayz_cool]

thanks

[@SaishreeLovesRawring]

Thank you i was so confused

[@carnosinehobs7759]

Praise the human who helped us actually understand math content in an education system that values marks over actually comprehension.

[@xcow3778]

Every nerds day: I have to watch this guy every single day Dumb kids: I don’t understand

[@zannaoutdoors]

thx that helped me alot now I am ahead of class! :)

[@HelloMyNameIsDORK007]

you probably dont need it anymore... but for future reference in case anyone else needs it, concave is when you can draw a line between two points and it goes outside the shape of the polygon. Convex is when you can draw a line between two points placed anywhere within the polygon and it doesnt leave the polygon.

[@eckoultimate]

(s-2)180 is the sum of the interior angles where s is the number of sides

[@1ronWinged]

Just use this formula (n-2) X 180 N will be the amount of sides the shape has.

[@yoface377]

AHAH Loool same My Unit Test is Tomorrow and this helped me out!!!!

[@luciusirving5926]

Thanks man! I needed this video for someone's Euclidean geometry lessons.

[@kavishkeswani8094]

i got a very important exam tomorrow and this channel always saves my grades. Khan Academy is goated on god

[@nar001]

Thank You so much! This helped me out a lot! Keep on doing videos like this

[@WilhelmScreamer]

Useful, I always forget this.

[@nazihaibrahim6537]

All of this went over my head.🤨

[@zert6719]

You go to my school

[@jisooteddykim]

Can't relate he's great 😭😭 !! Try againn

[@GiorgioCapocasa]

Thank you for these videos: I already knew this formula (like most of the people here, I think), but I've never been taught how this was derived. Please, keep on giving these awesome video-lectures :D

[@golrokhmoosavi6728]

I normally get ur videos but today I don't understand shit

[@luciusirving5926]

Euclidean geometry is very complex, even for average grownups. So therefore, I call Euclidean on this video.

[@Colindalugia]

so (s - 2) times 180 is the equation you were trying to get

[@musakhan3509]

I have test tomorrow and this is helping me out alot

[@CarDEL999]

I get the logic behind S-2; but in your polygon, couldn't you have created an additional two non-overlapping triangles?

[@taylorbrizee]

Thanks so much Saul! I am in 6th grade taking a 7th grade honors class, and I dont get it. I get it now!

[@lgryffindor18]

quad-er-aterol

[@wania7179]

Here's a formula you can use to find the sum of interior angles in a polygon= (N-2)×180 (N is the no. Of sides in the specific polygon. For example, if the polygon has 5 sides, we can subtract it by 2 and then multiply it by 180.

[@Liza-st4ut]

Thanks bestie😩 jisoo stans are heaven

[@wania7179]

@@Liza-st4ut LMAO youre welcome 😂😂💕

[@watcherzen]

thanks for all the geometry reviews. i'm actually taking the new GRE on Monday, and geometry has always been my worst area. Would be really nice if you can upload some videos about GRE strategies.

[@jisooteddykim]

This was 12 years ago WHATTTT

[@zinn.3576]

6:14 how many times did he sat "All sorts of crazy nez here" do tell me!

[@crowsnsuch]

a little bit of crazy

[@candyokeoma2596]

if you zoom in on 4.19 Its pentagon, you cand simply draw a line through the top to make a square (360) and a triangle (180) which adds up to 540

[@irasingh951]

I was so stressed when he missed the line n then he fixed it and I shouted “Thank you” really loaud and my dad looked at me as if I was crazy....

[@donutnarwhal135]

yea, it took him so long to figure it out

[@kevankwok01]

Sum of interior angles of a triangle is 180 Sum of square is 360 Sum of pentagon 540 Sum of hexagon 720 Sum of shape 369 (369-2)*180=66060 =18 =9 They all add to 9. Anyone know why that is the case?

[@nkelerasodi5382]

Such a life saver,

[@ryany2003]

U r amazing

[@midget7ina7greensuit]

Thank you helped alot

[@ageoberko6548]

Wow loved every detail of it! Amazing video ! 5 likes I will use it in my math test 10 likes I will write it in mi bedroom door

[@lamiyatarannum6079]

Okay, it's pretty cool. But what if we make it more crazier with s-2 overlapping and going outside the boundry? It happens when

[@maniingame6842]

(2n-4) × 90° for sum of internal ang and (2n+4) × 90° for sum of external ang (n= no. of sides)

[@moffyy]

at 6:29, it looks like a rose!

[@nocturnalvisionmusic]

Wow it does :D

[@nicoledouglas2896]

What do you get if you divide 180° by the number of angles? Does that do anything?

[@JohnnyLion66]

Thank you very much!!

[@sameerakhan8893]

Thanks it help🙂🙂🙂🙂

[@sourpatchkid311]

This is still confusing

[@spencerwang1088]

Get paper and cut it into the shape you want. Than, cut the shapes into triangles. we know that 1 triangle is a total of 180, so you take how many triangles you have, times it by 180, and you get the total number of degrees of the shape you made!

[@haihaiiro]

Just make sure when proving it, don't have a overlapping triangle. It will mess things up.

[@evanbreyer4793]

DUDE WHAT TYPE OF A HEXAGON IS THAT I GOT MORE TRIANGLES THEN YOU DID WTF

[@starplatinum3373]

stfu

[@sourabhbatra397]

Very nice.... Understanding works

[@eatcarpet]

This video has all sorts of craziness.

[@nusaibafatima1324]

thanks alot for the help it was helpful

[@shereen8400]

if the sum of measure of the interior angles of a regular polygons equals 180(n-2) where n is the number of its sides,then the measure of the interior angle in radian of a regular pentagon equals..... (π/3 or 7π/2 or 3π/5 or 2π/3)

[@RichGuy1]

is the last 102 just an example? and the result of the correct decagon is 1440, right, even though it's irregular??

[@kechunmerriweather8739]

thank!

[@richxrdabraham]

This so amazing.

[@sickstuffsocal222]

You know what’s even more amazing? Forcing your stuffed animal to vape.😏

[@Theparentcloset]

This helped my daughters.

[@lilromain101]

This video brought my OCD on edge. Nice explanation though

[@armandomartinez9471]

When is the english version coming out?

[@edwinr4378]

Awesome 👍

[@dedurps8227]

Im trying to find the measure of the interior angles if they are not equilateral

[@PKruzen]

So the general formula here for Sum of interior angle = (# of sides x 180) ?

[@xzandermccoy9922]

Soooo helpful

[@aaronmanzo1684]

Thank u

[@urlovekel]

yeah right now i’m thinking why u have to minus two. (sum is n-2 x 180)

[@ahmadhilmy9637]

Or you can take the number of sides and subtract it by 2

[@cyberprodigy]

That's nice thing to know.

[@manchildx4263]

Thx

[@brennan2185]

Using this formula on your website I got a 5 sided polygon with 540 degree total, and another time with 360 degree total; I got a 6 sided polygon with a 720 degree total, and another time with a 360 degree total; a 7 sided polygon with a 900 degree total and another time with a 360 degree total. When do we know when to use this formula or not? How are we supposed to know that all the outside angles are equal to 360 degrees if there is no value for any inside or outside angle?

[@atharvanagdeve1992]

HEY! DONT READ THE COMMENTS!! GO UP AND STUDY !!

[@patriocabello841]

No

[@aspenfilms4292]

wow awesome video!

[@justinmaduako4315]

((Polygon's a plane figure with at least three straight sides 'n angles, 'n typically five or more (➕➖✖➗👨‍🔬👩‍🔬📚🏫); Sincerely, Justin Maduako)).

[@sleepykristato1481]

( - 2) ×180 is a simpler way of doing it

[@Watcharintrawut]

lol crosshair on fps games :3

[@shailenderkalia8344]

Loved it sir

[@prakashmishra2026]

they should not be overlapping thats all what i need

[@jisooteddykim]

I have my exam tomorrow pray for Me to pass 😭😭!!

[@aouzr_rl-PK]

Oh same lol are you from BSS school? Cause Iam

[@jisooteddykim]

@@aouzr_rl-PK not even close I m from Pakistan karachi

[@aouzr_rl-PK]

@@jisooteddykim wth same

[@jisooteddykim]

@@aouzr_rl-PK which school

[@aouzr_rl-PK]

@@jisooteddykim beconhouse

[@asahizlx5131]

This really helped alot but the problem is We forget easily....

[@jisooteddykim]

Jbhhh!!😭😭

[@zalama61]

he is well better in confusing others!!! Show each step please

[@lindaroji5158]

Sir I have a doubt please slove this sum of interior angles 3 4 5 6 7 8 9 10

[@bosssakuka3402]

I think you got something wrong. Your 'crazy shape does not include 4 triangles on the crazy side at 6 minutes and 19 seconds

[@meredithfrost929]

It was very helpful, but math is not my favorite

[@ARSEnal1Wojciech]

math is fun look pacman at 6:05

[@mariahspalace3782]

WSW ARSFC haha… I found it. 😂

[@Bino.Automation]

Hehe

[@sleepykristato1481]

nice

[@SAADGAMING-uo9yi]

Where did 4 come from around 8:20?

[@EliWli_]

Is no one gonna talk about his voice? :^

[@jerfersonmatos28]

Alright, if a triangle has 'x' sides, it will have 180*(x-2) °. Now I just have to remember

[@bread1302]

You could have explain it a little slower and simplier to understand for the non native english speaker.

[@JohnnyLion66]

I am having a lot of trouble trying to figure out the difference between a convex and a concave. Are there any concaves in the lesson? I know what he's saying. A concave is a shape that has angles that go the opposite direction of what the rest of the angles are going. I need to know the difference between a 360 and other shapes. And he just doesn't give me enough information in this video.

[@vampirehannahrocks]

Hayyyyyyyyy.... #Mrs.Johnsons class

[@nadamenos32]

in the formula s-2 what does the s mean and what does 2 mean

[@ky_ne04]

Nada Menos the number of sides minus 2 (example: 9-2)

[@zayan155]

Thank you very much ! ! ! This helped me very much :)

[@thelibrother3596]

he messed up at 7:43. If you count the purple lines carefully there are actually 5 lines. if anyone agrees then reply to me or tell me if i'm wrong

[@noralyounes214]

he saw it after that

[@zk2741]

No hes not counting the lines hes counting the triangles

[@syedaemaan43]

this was legit 4 years after i was born-

[@jisooteddykim]

WOWW

[@IzzyBradley]

What if it's a 9 side regular polygon? You can't get all triangles in the polygon. In the end it's left with a few triangles and a different shape.

[@thequeen5542]

Is it always minus 2?

[@Rasayandev]

Hey dude I want to make KZbin videos like you .....I like it ....so please tell me how to make this literally I have no idea about this .....

[@jisooteddykim]

Bro you can !! It would subscribe

[@RobbertKooiman]

What program do you use for these video's? I guess you're using a bamboo tablet?

[@raynali2054]

What is this app called?

[@cinnamoroll1981]

its their app i think so

[@davidvillarroel1654]

Generally, an S-sided polygon has how many degrees??

[@chronoshade1286]

David Villarroel it's a variable. S is a variable

[@lee_xanna]

so... how would you work out a question like this: the sum of interior angles of a polygon is 9000 degrees. How many sides does the polygon have?

[@lee_xanna]

***** thanks :)

[@trickmaster32]

***** (n-2)x180=angle sum

[@okaya1463]

my brain stopped at 8:10

[@DeepakKumar-pk1th]

Why a+b+c only =180 degree not other why bad only

[@fancyfox4958]

cant you just add up all the four sides of the four sided and three sided shape and get 360 or 180??

[@montefrancis369]

No, because not all polygons are 4 sided. But yes. with four-sided shapes. you can. It's just much harder to show in your working out