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

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  • Опубліковано 27 жов 2024

КОМЕНТАРІ • 219

  • @ClemoTekkerz
    @ClemoTekkerz 7 років тому +40

    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!

  • @kylemichael110
    @kylemichael110 7 років тому +49

    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 :)

  • @mariahspalace3782
    @mariahspalace3782 7 років тому +86

    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.

  • @Jenny-tu9fc
    @Jenny-tu9fc 5 років тому +70

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

  • @jesuisbobbyy
    @jesuisbobbyy 9 місяців тому +1

    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).

  • @GlowtreeMC
    @GlowtreeMC 12 років тому +10

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

    • @miiiiiiraaa
      @miiiiiiraaa 4 роки тому +1

      GlowTree omg that’s 7 years ago !!

    • @catsrepic8813
      @catsrepic8813 4 роки тому

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

    • @vontae393
      @vontae393 3 роки тому

      @@catsrepic8813 OMG ITS BEEN 2 MONTHS AGO

    • @Sienna850
      @Sienna850 3 роки тому

      How’s life now? This was 8 years ago

    • @luviesni-ki5696
      @luviesni-ki5696 3 роки тому +1

      your 21 now

  • @itsclarencetong
    @itsclarencetong 11 років тому +25

    Please never stop making maths videos, I just subscribed!

    • @asemaldaras6687
      @asemaldaras6687 4 роки тому +1

      your now a dad ...

    • @NoahMine1
      @NoahMine1 4 роки тому +1

      Bro it’s 7 years

    • @mariasullivan493
      @mariasullivan493 4 роки тому +2

      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
      @sma530v8 4 роки тому

      ok

    • @1Tara
      @1Tara 3 роки тому

      @@NoahMine1 8 now

  • @carnosinehobs7759
    @carnosinehobs7759 3 роки тому

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

  • @HelloMyNameIsDORK007
    @HelloMyNameIsDORK007 12 років тому

    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.

  • @brookethompson7115
    @brookethompson7115 6 років тому +6

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

  • @joeytierney7455
    @joeytierney7455 8 років тому +28

    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
      @luciusirving5926 5 років тому +1

      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
      @trx3640 3 роки тому

      @@luciusirving5926 what are you even talking about

  • @kavishkeswani8094
    @kavishkeswani8094 Рік тому

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

  • @musakhan3509
    @musakhan3509 2 роки тому

    I have test tomorrow and this is helping me out alot

  • @zannaoutdoors
    @zannaoutdoors 12 років тому +4

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

    • @hadya8518
      @hadya8518 Місяць тому

      I wonder where you are rn

  • @eckoultimate
    @eckoultimate 11 років тому +3

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

  • @watcherzen
    @watcherzen 13 років тому +1

    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.

    • @Lifebutdeeply
      @Lifebutdeeply 10 місяців тому

      This was 12 years ago WHATTTT

  • @yoface377
    @yoface377 12 років тому +3

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

  • @wania7179
    @wania7179 4 роки тому +1

    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
      @Liza-st4ut 3 роки тому +1

      Thanks bestie😩 jisoo stans are heaven

    • @wania7179
      @wania7179 3 роки тому

      @@Liza-st4ut LMAO youre welcome 😂😂💕

  • @nar001
    @nar001 4 роки тому +1

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

  • @WilhelmScreamer
    @WilhelmScreamer 13 років тому +2

    Useful, I always forget this.

  • @GiorgioCapocasa
    @GiorgioCapocasa 13 років тому +3

    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

  • @luciusirving5926
    @luciusirving5926 5 років тому +2

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

  • @sameerakhan8893
    @sameerakhan8893 3 роки тому +1

    Thanks it help🙂🙂🙂🙂

  • @sourabhbatra397
    @sourabhbatra397 6 років тому

    Very nice.... Understanding works

  • @taylorbrizee
    @taylorbrizee 13 років тому +2

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

  • @midget7ina7greensuit
    @midget7ina7greensuit 11 років тому +1

    Thank you helped alot

  • @nkelerasodi5382
    @nkelerasodi5382 5 років тому +1

    Such a life saver,

  • @1ronWinged
    @1ronWinged 4 роки тому +1

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

  • @candyokeoma2596
    @candyokeoma2596 3 роки тому

    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

  • @nusaibafatima1324
    @nusaibafatima1324 3 роки тому

    thanks alot for the help
    it was helpful

  • @maniingame6842
    @maniingame6842 3 роки тому

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

  • @xcow3778
    @xcow3778 3 роки тому +7

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

  • @CarDEL999
    @CarDEL999 7 років тому +1

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

  • @JohnnyLion66
    @JohnnyLion66 12 років тому

    Thank you very much!!

  • @richxrdabraham
    @richxrdabraham 4 роки тому +1

    This so amazing.

    • @sickstuffsocal222
      @sickstuffsocal222 3 роки тому

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

  • @edwinr4378
    @edwinr4378 4 роки тому

    Awesome 👍

  • @ryany2003
    @ryany2003 11 років тому +2

    U r amazing

  • @Theparentcloset
    @Theparentcloset 4 роки тому

    This helped my daughters.

  • @nazihaibrahim6537
    @nazihaibrahim6537 6 років тому +15

    All of this went over my head.🤨

    • @zert6719
      @zert6719 4 роки тому

      You go to my school

    • @Lifebutdeeply
      @Lifebutdeeply 10 місяців тому

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

  • @xzandermccoy9922
    @xzandermccoy9922 4 роки тому

    Soooo helpful

  • @lamiyatarannum6079
    @lamiyatarannum6079 4 роки тому

    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

  • @aspen_films
    @aspen_films 9 років тому

    wow awesome video!

  • @cyberprodigy
    @cyberprodigy 13 років тому

    That's nice thing to know.

  • @nicoledouglas2896
    @nicoledouglas2896 8 років тому +1

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

  • @shailenderkalia8344
    @shailenderkalia8344 6 років тому

    Loved it sir

  • @zinn.3576
    @zinn.3576 4 роки тому +3

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

  • @kevankwok01
    @kevankwok01 Рік тому

    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?

  • @lgryffindor18
    @lgryffindor18 11 років тому +13

    quad-er-aterol

  • @kechunmerriweather8739
    @kechunmerriweather8739 10 років тому +2

    thank!

  • @armandomartinez9471
    @armandomartinez9471 4 роки тому

    When is the english version coming out?

  • @golrokhmoosavi6728
    @golrokhmoosavi6728 8 років тому +37

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

    • @luciusirving5926
      @luciusirving5926 5 років тому

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

  • @RichGuy1
    @RichGuy1 Рік тому

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

  • @eatcarpet
    @eatcarpet 12 років тому +2

    This video has all sorts of craziness.

  • @Colindalugia
    @Colindalugia 9 років тому +6

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

  • @aaronmanzo1684
    @aaronmanzo1684 4 роки тому

    Thank u

  • @brennan2185
    @brennan2185 11 років тому +1

    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?

  • @shereen8400
    @shereen8400 7 років тому

    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)

  • @moffyy
    @moffyy 5 років тому +1

    at 6:29, it looks like a rose!

  • @manchildx4263
    @manchildx4263 4 роки тому

    Thx

  • @ageoberko6548
    @ageoberko6548 7 років тому +3

    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

  • @PKruzen
    @PKruzen 12 років тому

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

  • @irasingh951
    @irasingh951 6 років тому +6

    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....

  • @zalama61
    @zalama61 7 років тому

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

  • @sourpatchkid311
    @sourpatchkid311 11 років тому +10

    This is still confusing

    • @spencerwang1088
      @spencerwang1088 6 років тому +2

      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
      @haihaiiro 4 роки тому

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

  • @Lifebutdeeply
    @Lifebutdeeply 10 місяців тому +2

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

    • @aouzr_rl-PK
      @aouzr_rl-PK 10 місяців тому

      Oh same lol are you from BSS school? Cause Iam

    • @Lifebutdeeply
      @Lifebutdeeply 10 місяців тому

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

    • @aouzr_rl-PK
      @aouzr_rl-PK 10 місяців тому

      @@Lifebutdeeply wth same

    • @Lifebutdeeply
      @Lifebutdeeply 10 місяців тому

      @@aouzr_rl-PK which school

    • @aouzr_rl-PK
      @aouzr_rl-PK 10 місяців тому

      @@Lifebutdeeply beconhouse

  • @asahizlx5131
    @asahizlx5131 4 роки тому

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

  • @zayan155
    @zayan155 11 років тому

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

  • @evanbreyer4793
    @evanbreyer4793 8 років тому +14

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

  • @dedurps8227
    @dedurps8227 3 роки тому

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

  • @vampirehannahrocks
    @vampirehannahrocks 9 років тому

    Hayyyyyyyyy.... #Mrs.Johnsons class

  • @urlovekel
    @urlovekel 3 роки тому

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

  • @lilromain101
    @lilromain101 9 років тому +1

    This video brought my OCD on edge. Nice explanation though

  • @lindaroji5158
    @lindaroji5158 4 роки тому

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

  • @ahmadhilmy9637
    @ahmadhilmy9637 2 роки тому

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

  • @JohnnyLion66
    @JohnnyLion66 12 років тому

    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.

  • @raynali2054
    @raynali2054 6 років тому

    What is this app called?

  • @prakashmishra2026
    @prakashmishra2026 6 років тому

    they should not be overlapping thats all what i need

  • @sleepykristato1481
    @sleepykristato1481 5 років тому

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

  • @lee_xanna
    @lee_xanna 10 років тому

    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?

  • @marvinmichael1925
    @marvinmichael1925 5 років тому

    if n is no of sides the sum of interior angles is (N - 2)×180 degrees
    in a triangle it is (3 - 2)×180= 180
    a quad (4-2)×180 =360
    a decagon (10-2) ×180= 1440

  • @SAADGAMING-uo9yi
    @SAADGAMING-uo9yi 5 років тому

    Where did 4 come from around 8:20?

  • @THEGnade2000
    @THEGnade2000 10 років тому

    just wondering if you guys took geometry in 10th grade or 9th grade

  • @davidvillarroel1654
    @davidvillarroel1654 8 років тому

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

    • @chronoshade1286
      @chronoshade1286 7 років тому +1

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

  • @nadamenos32
    @nadamenos32 7 років тому

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

    • @ky_ne04
      @ky_ne04 7 років тому +2

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

  • @Rasayandev
    @Rasayandev 6 років тому

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

    • @Lifebutdeeply
      @Lifebutdeeply 10 місяців тому

      Bro you can !! It would subscribe

  • @bosssakuka3402
    @bosssakuka3402 4 роки тому

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

  • @Studious4Health
    @Studious4Health 10 років тому +6

    math is fun look pacman at 6:05

  • @zoranencharity3854
    @zoranencharity3854 4 роки тому +1

    Mad ooooooo

  • @IzzyBradley
    @IzzyBradley 11 років тому

    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.

  • @EliWli_
    @EliWli_ 4 роки тому

    Is no one gonna talk about his voice? :^

  • @fancyfox4958
    @fancyfox4958 6 років тому

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

    • @montefrancis369
      @montefrancis369 5 років тому

      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

  • @thequeen5542
    @thequeen5542 5 років тому

    Is it always minus 2?

  • @justinmaduako4315
    @justinmaduako4315 Рік тому

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

  • @RobbertKooiman
    @RobbertKooiman 13 років тому +2

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

  • @DeepakKumar-pk1th
    @DeepakKumar-pk1th 7 років тому

    Why a+b+c =180.

  • @jerfersonmatos28
    @jerfersonmatos28 6 років тому

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

  • @DeepakKumar-pk1th
    @DeepakKumar-pk1th 7 років тому

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

  • @okaya1463
    @okaya1463 6 років тому

    my brain stopped at 8:10

  • @Watcharintrawut
    @Watcharintrawut 12 років тому +2

    lol crosshair on fps games :3

  • @bread1302
    @bread1302 3 роки тому

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