How would you prove that the sum of the interior angles of a n-gon is 180(n-2) degrees in the case that at least one of the interior angles is greater than 180 degrees?

Question

anonymous · Answer

Basically how would you prove the case where its a concave polygon? You wouldn't always be able to create a line segment that can connect any two vertices

ganeshie8 · Answer

like for example

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?

anonymous · Answer

Yeah, exactly.

ganeshie8 · Answer

It will be easy to prove if we consider "signed" angle for sum of exterior angles of a polygon

ganeshie8 · Answer

I'm thinking of using the fact that the sum of "signed" exterior angles of any polygon add up to 360

ganeshie8 · Answer

count counterclockwise as positive and clockwise as negative

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