# Visual demonstration that all angles of a shape combine to make 360 degrees

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# Visual demonstration that all angles of a shape combine to make 360 degrees

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Exterior angles, that is.

As former geometry teacher, I feel like I need to note that this is only true for convex polygons. Concave and self-intersecting polygons are built different.

Yep, came here to point this out, still burns after I made the mistake in a test over 50 years ago!

Im not good at geometry lol

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They aren't even full external angles, though

I like how 'angles' needed further detailing, but 'a shape' apparently didn't.

What about the angles on the inside?

(n-2)180= sum of the interior angles

Since the exterior angles add up to 360 and there are n number of angles where each interior + exterior angle adds up to 180, subtract 360 from n*180 to get the sum of the interior angles.

The angles inside the triangle add up to 180 degrees. There is a nice geometric proof of this (draw a line parallel to the triangle base, going through the triangle tip, then identify angles which are equal to each other. Sorry if this isn't clear, if I had a diagram it would be.)

Triangle’s interior angles add to 180. It goes up by 180 for every additional side. Square is 360, pentagon 540.

that's just cool... It's funny, I was always more of an English/History kind of nerd, but I really loved geometry, it was just a fun "you can see it" form of math that I really enjoyed.

Geometry was the original way (in ancient Greece etc...) to prove maths theorems.

Imo it's one of the best ways to teach kids problem solving and critical thinking.

Same

calculus can be visual as well. derivatives and integrals can be seen with the polynomial function on a plot

Visual demonstration that all angles of a shape combines to make 360 degrees *

it’s a good rule tho

If it was longer it could show you how many degrees the sums of internal angles are. For regular polygons:

I understood the word "shape".

All these geometry pros dont need this, but I definitely do

Walk in a line and then turn and turn again until you get back to the same spot, by definition you have rotated 360 degrees

And walk away?

If you don't turn around when you get back to where you started, then you've only rotated 180 degrees.

Hello, is there any social media account to learn math in a fun way? Thanks.

i like watching Eddie Woo on youtube. he explains things like why dividing by zero doesn't work, and why the pythagorean theorem is a thing, and lots of similar stuff

You could try

My god.

It's Jason Bourne!

In my 29 years of life I've had the WORST time trying to figure it this. You just did want every teacher Ive ever had tried to do, make me understand this.

Wait, so it’s all circles?

It’s all TRIANGLES

Supplements of angles of a convex shape combine to make 360 degrees.

Not all angles, only exterior angles. And not all shapes, only convex shapes. Overall, shit caption

This is very helpful

Idk why I’ve never thought abt this but it makes complete sense

Geometry is actually so amazing and cool. I love it.

This is beautiful and makes me want to pick up geometry as a hobby. Thanks for posting!

How simple it would it have been for my lazy high school geometry teacher to show us this

I mean yeah if the shape connects it has to essentially go in a circle

My butthole loosing up throughout college years

Pics?

Science, bitch. Damn yeah Mr White.

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This only works for concaves.

exterior

This is like a common knowledge that you learn in primary schools

Conceptually sure but I don't remember it being taught visually like this at least. I thought it was neat.

Still cool to visualize it like this

In America??

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Geometry makes so much more sense now...

Man I wished they showed me this in school

Why comes it do dat

Wouldn't you burn in 360 degrees

Holy shit

Dude your title is not correct. Sum of exterior angles.

nice visualization, i always understood this as a car going along the perimeter always takes a 360 turn, works even for concave shapes

Duh

This could have been so helpful in math growing up!!

**Enclosed shape

Addition. This cool new invention

Damn!

Least interesting

I always thought of them like circles with flat edges, it all equals 360

If my teacher had shown me this when I was in geometry, maybe I would have understood it sooner lol

So does this prove that all shapes are just low resolution circles?

Ok, probably a stupid question: If these were three dimensional objects, would those angles form a sphere?

Angles can’t really be measured across all the dimensions at a point in a 3D space, as they would normally measure between two lines on a 2D plane.

This is one of those things that’s factually true but when I hear and see it my brain goes “should not work”

Giving me Vietnam flashbacks from Geometry class.

The Divine Pizza

BURN THE WITCH

But what about in 3D ;)

Holy shit this blew my mind... If I were still in school I'd be showing everyone

What the hell? All this shows is that if you travel around an object, you turn 360 degrees.

Now do it with non-Euclidean geometry

Everything is a circle. nothing is straight. My life is a lie.

I knew it as a rule, but to see it play out in picture is something I've never thought of ... think of all the people that will be helped with this visualization!

They should show these at school this makes it very easy to understand

"Cut my life into pieces"

Woah, man

This was one of the things that made me love geometry so much.

Now do 3d shapes.

Well yeah, of course, there is only 360 degrees of motion any straight line can travel in our dimension. It all starts from 1 point.

Ahhh…SOHCAHTOA

Lesson of the day:

Genuinely curious, is this only true when the lines go in the direction necessary to enclose itself?

Mind blown

That’s acute.

What website is this from?

This is how you use a computer to teach!

Oh this turned me on

Wonder what software was used to make this. Very cool. Thanks

दुनिया गोल है!

Proofs are the worst part of geometry

this is streets ahead

I just know theres probably a whole branch of mathematics devoted to this, probly called Trigonometry 2.

Do it with a circle!!!

Damn that is interesting hah

Circle: The ultimate shape

Oh! External angles. That does not work with the angles in the inside lol

Ima send this to my idiot teacher

Why is primary/middle school math interesting?

“Because, it’s a circle”

gave me a math boner

I wish we had representations like this when I was in school. I thought I was bad at math my whole life, but then I realized it was more the fact that I’m more of a linguistic and conceptual person.

That's just poof

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It's not really interesting it's just basic knowledge

I feel like this can be said about anything 3 dimensional or am I just high

All normal polygons are circles. Got it

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I feel silly for not knowing this.

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Makes me wish the obvious relationship between mathematics and art was made more prominent in school, it would likely help inspire many kids about the fascinating nature of mathematics 🤓🤌

If all the outer edges make up 360 degrees, what do the inner edges amount too? (Serious question)

why do we need to know this ?

Isn't this totally obvious?

Where was this in my high school math class?

Watched that 3blue1brown video, so this makes me itch a bit

Why shit like this isn't shown in schools.

Do a circle

I learned this in high school geometry, but wish I'd had a visual like this to make me believe it. I thought algebra and geometry were 100% alternative facts (before that phrase existed), so I treated both classes like I was learning a foreign language and that lowered my stress level.

they skipped square for a reason 😂

90 x 4 is 360

It still work on a square tho

That’s rad

All polygons at least, right? Lines are shapes and some shapes have curved lines where this isn’t true. And that’s only 2D shapes. Sorry I’m very literal.