Sum of the exterior angles of convex polygon | Geometry | Khan Academy

More elegant way to find the sum of the exterior angles of a convex polygon

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[HigherPlanes]

I wish you could have been my teacher in middle school. You're awesome Sal

[toplobster]

You're great at explaining things! So easy to understand. Thanks!

[WSCOMPUTER]

Sal, I came up with a very simple solution:
5*360-3*180-5*180=360
5*360 --- all five full angels
3*180 --- (n-2)*180 - all 5 internal angles
5*180 --- 5 adjacent external angles.
So a general rule would be: n*360-(n-2)*180-n*180=360 Q.E.D.
If you find useful you can make a video on it :)
KHANACADEMY - best school on Earth.

[alisonbrown]

anyone here cause of the coronavirus or is it just my school

[justinmaduako]

((Man, I just love watching those Khan Academy videos (➕➖✖➗👨‍🔬👩‍🔬📚🏫); Sincerely, Justin Maduako)).

[Basic]

So it's not applicable for concave polygon ??

[thisshouldsayK]

@smicha7 It's easier for me to just remember that a convex polygon's outer angles will total 360°.

[wania]

Thank you so much! This cleared my concept :)



Btw anyone got this assignment from online school? :' (I got a test which includes this T_T)

[jaleahmad]

May I know the software and hardware that you use to draw the diagrams in your video?

[brennan]

I am having the same problem I have done dozens and dozens of problems and the answers seem to be rather arbitrary. It doesn't stick to the formula(s) that is provided.

[karmaakabane]

So this guys just knows everything huh

[WSCOMPUTER]

@thisshouldsay2K You are right, but I meant a proof, not something to remember.

[JohnnyLion]

But Sal, NONE of the polygon in the "Angles of a Polygon" exercise don't seem to be concave.

And some of the polygons used in the exerciise don't look anything like a 360 degree polygon, but the answer to the problem on just about every other problem is 360 degrees. So, how do I know when to apply this "elegant" way?

[ajitkumar-mubp]

it has three lines coming out from one point

[thisshouldsayK]

@smicha7 Ah. Well yeah, then that will work.