Question 1101781: What is the sum of the exterior angles of a convex polygon with 100 sides ?
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443)   (Show Source):
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! An exterior angle of a polygon is the change of direction needed at each vertex to go around the polygon.
For example, here is a hexagon, with one of its exterior angles labeled:
 .
For that particular polygon in my drawing,
if you go around its perimeter counterclockwise,
you have to veer  left at each vertex.
For this convex polygon,  ,
going around its perimeter counterclockwise, you would veer left at each corner by  .
Of course, when you drive ome whole turn around a block like that,
and end up in the same direction you started,
the sum of all the turning angles is  .
That works for every convex polygon.
If you were going around the perimeter of a concave polygon,
one with a "cavity" like this one,
 you would be making left turns and right turns,
and wondering if it would be possible to go straight line between A and C,
not passing through B.
We could say that the difference betweem
the sum of angles for the left turns,
and the sum of angles for the left turns,
but it gets complicated,
and that is why we do not like concave polygons.
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