A rule of polygons is that the sum of the exterior angles always equals 360 degrees, but lets prove this for a regular octagon (8-sides).

You are watching: Sum of exterior angles of a octagon

First we must figure out what each of the interior angles equal. To do this we use the formula:

((n-2)*180)/n where n is the number of sides of the polygon. In our case n=8 for an octagon, so we get:

((8-2)*180)/8 => (6*180)/8 => 1080/8 = 135 degrees. This means that each interior angle of the regular octagon is equal to 135 degrees. 

Each exterior angle is the supplementary angle to the interior angle at the vertex of the polygon, so in this case each exterior angle is equal to 45 degrees. (180 - 135 = 45). Remember that supplementary angles add up to 180 degrees. 

And since there are 8 exterior angles, we multiply 45 degrees * 8 and we get 360 degrees.

This technique works for every polygon, as long as you are asked to take one exterior angle per vertex.

Upvote • 3 Downvote
Comments • 5

Smith J.

Either I don"t understand your reasoning or you are talking bollocks. The INTERIOR angles add up tp 1080 in a polygon, ie 135 each.

Jaycee D.

All you have to do is divide 360/n, n being the number of sides in the polygon

Jeanetto L.

I agree with the first person. it IS 135!!!

Emily M.

Its wrong the answer is 45, all you have to do it take 360 and divide it by the number of sides (360/n) so lets say that the number of sides is 6, your equation would be 360/6 which would be and the answer would be 60. Check my math if you don"t think I"m right.

JAde W.

This helped me so much thank you 

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