Challenging triangle angle problem | Angles and intersecting lines | Geometry | Khan Academy

[@peterthegreat996]

I initially used some geometry to get to the 540 part, but what I like about Sal is that he uses arithmetic and Algebra to subsequently derive the formula , he is able to put numbers where there are no numbers using geometry but at the same time use the algebra- he is putting us the mind of Euclid. Really good stuff, btw he does this in his physics classes and economic classes. It's like he is increasing the horsepower of and engine but in this case our minds our the engine.

[@kenmeyer100]

A much simpler way would be to imagine that you are walking along all the polygon lines once until you face the original direction. Then logically you turned 360 degrees. That's exactly the sum of all exterior angles. Why? At each turn you change your direction by exactly the exterior angle given at that turn.

[@sabrigiray]

Total of exterior angles of any kind of polygon is equal to 360. Doesn't matter if it's triangle, square, pentagon or heptagon. Just saying.

[@elinag5743]

I don't know if it's just me, but on the KA website, this video cuts off at 6:25. Luckily the entire video is on KZbin, so I can finish it. Also, thank you Sal! You're a great teacher!

[@SantosSantos-bf1fe]

Same!

[@teamkobeforlife1960]

use the formula for finding interior angle for any polygon (n-2)180 where n is the number of sides in the polygon

[@tommydashed4205]

Super late reply but all formulae came from somewhere. They didnt just appear. Students of KA getting to this video will not have learned that formula yet.

[@IQWiz]

There is a much easier way to solve this problem! The sum of all the angles in a pentagon is 540. The sum of all the supplementary angles is 5 x 180 = 900. 900 - 540 = 360!

[@renewd]

The easiest way would be to just say that the sum of the exterior angles of every polygon equal 360 degrees. That is true, but how much fun would that be?

[@lucasvegezzi8736]

Megane Thomas if u didn’t now that u wouldn’t now how to use letters as u learn degrees in shapes before using sum also u wouldn’t be able work out this sum

[@tommydashed4205]

@@lucasvegezzi8736 yes you would. He used algebraic ideas combined with very simple geometry to solve the problem. You learn algebra before geometry and this kind of problem is exactly why.

[@superultramegaweird]

This video is very helpful! I just wish I'd seen in before I took the GRE. I missed a question exactly like this! Khan Academy ROCKS!

[@Consquisitor]

(n-2) x 180 n is the number of sides in the shape the shape had 5 sides, and 5 subtract 2 is 3. 3 x 180 = 540

[@SaishreeLovesRawring]

Wdym-

[@YamaanAli-f4r]

excluding the sum of interior angles & sum of exterior angles there is another way we can see that line cd & ab are parallell so extend every line till it makes vertical angles,suplementary angles and triangles then simply use the properties to find the angles You will see that: c+b=180 a+d+e=180 so A+B+C+D+E=360

[@ggmm117]

Thanks for the angle videos, They're awesome, and very helpful. Also can you do a section on polynomial functions because the the ones you currently have aren't that directly focused on beginners polynomial function.

[@paulakiaraluna1969]

it was easier how my teacher explained it to us but this one is pure logic. just magnificent o.o

[@rajaarveti]

Thank you for the help. I got a 100 percent on my math test yesterday and I told my teacher that you helped me. Thank you for the support

[@chiefsed4473]

This deserved a few thousand likes

[@光-p9x]

That's really helped! ❤❤

[@DehXable]

If you identify early on that the sum of the interior angles is simply 3 * 180, the problem becomes 5*180 - 3*180 = 2 * 180 = 360 without needing to break up the interior angles into smaller parts.

[@medhasarker6967]

Thx

[@liamstephenson106]

This is brilliant. Helped me as I understand so much better

[@HandsomeDevil456]

The way I figured it out is all 5 lines equal 900 degrees. There's 3 triangles inside which is 540 degrees. 900 - 540 = 360. Additionally, every new side added to a polygon creates a new triangle. So sum of exterior angles = 180 * sides - 180 * (sides - 2). Which reduces to 180 * sides - 180 * sides + 360. Which then reduces to sum of exterior angles = 360. So no matter the amount of sides, the sum is always 360.

[@shadowdude217]

Very interesting problem! keep up the good work!!! :)

[@unchained_bootaga403]

that's exactly why I love math

[@KawaiiAznPanda7]

my math teacher uses your videos

[@datzan]

You sound like the narrator on How i met your mother!

[@CaesarCapone]

Is there a video then on how to solve the angle measure of each of a, b, c , d, e individually; or is it not possible? I would think it would be... Anybody?

[@123123mike]

Crazy! Who the heck was the first to figure this stuff out?? lol

[@THEROCKETSUMMERL0VER]

KHAAAAAAAAAAAAAAAAN!!!

[@bennettcox5958]

Imagine watching this because u wanted to 😂

[@saidurrahmanmj8569]

SO difficult you made. I Have easy way

[@samuelwillamson1749]

Low-poly sonic.

[@atharvanagdeve1992]

I am running out of colors!! xD lol

[@PedrinhoCruzeirense]

Easy - all we need to do is SUBTRACT the UNWANTEDE ANGLES from the TOTAL SUM of all the angles in this picture. And it can be made visualy. We have 5 points, each of them have 360º around (duh!). So, the total of all angles is 1800º. We see that we have 5 big external angles of 180º (one at EACH POINT of the figure), and these angles must be subtracted from the total, cuz we want just the sum of the minor external angles. So, we have 5 angles of 180º that sum 900º. We will subtract 900 from 1800º. We have now a subtotal of 900º. Now, we just need to get rid of the internal angles of the pentagon. And we know that the sum of the internal angles of any pentagon is 540º (see note #1 below). So, after we rip these 540º from 900º, we have the result: 360º. ==== Note #1 At least here in Brazil, when we are little kids we learn that the sum of internal angles of every triangle is 180º. And we learn a "shortcut" to find the sum of internal angles of any polygon: we just need to add 180º for each side we "add" to the original polygon. So, if with 3 sides we have 180º, with 4 we have 360º, with 5 we have 540º, with 6 we have 720º, with 7 we have 900º, and so on... Note #2 The method used by the author is very instructive and full of details, but it is making simple things look too complicated. The apporach used by me takes much less calculations and, as a plus side, it stimulates the viewer to understand subtraction and addition in a visual manner - what, from my experience, many people unfortunately don't understand, what makes them strugle painfuly with simple problems involving area of polygons and volume of solids, for example. I suggest the author to rename the video title, cuz this problem isn't that challenging at all - it's actually quite simple... No ofense, don't take me wrong, please. ;-)

[@jerfersonmatos28]

Pedrinho Paquiderme escreva em português aí pra eu entender melhor

[@crontsquared230]

How come you had to use three triangles? Why not two or more? I am confused! Any help would be appreciated

[@zoe-bm9sc]

Cront Well, you have to use an amount of triangles that fits in and doesn't overlap. The lines should reach from angle to angle. I hope this helps.

[@zphoaloo]

2024