A rule of polygons is that the amount of the exterior angles constantly equates to 360 degrees, yet lets prove this for a continuous octagon (8-sides).

You are watching: What is the exterior angle of an octagon

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

((n-2)*180)/n wbelow 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 suggests that each inner angle of the continual 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 situation each exterior angle is equal to 45 levels. (180 - 135 = 45). Remember that supplementary angles include as much as 180 levels. 

And because there are 8 exterior angles, we multiply 45 levels * 8 and we obtain 360 degrees.

This method functions for eextremely polygon, as lengthy as you are asked to take one exterior angle per vertex.

Upvote • 3 Downvote
Comments • 5

Smith J.

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

Jaycee D.

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

Jeanetto L.

I agree with the initially perchild. it IS 135!!!

Emily M.

Its wrong the answer is 45, all you need to carry out it take 360 and also divide it by the variety of sides (360/n) so lets say that the variety of sides is 6, your equation would certainly be 360/6 which would certainly be and also the answer would certainly be 60. Check my math if you do not think I"m best.

JAde W.

This assisted me so much say thanks to you 

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