A dominance of polygon is that the sum of the exterior angles always equals 360 degrees, however lets prove this for a continual octagon (8-sides).

You are watching: What is the measure of an exterior angle of a regular octagon?

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

((n-2)*180)/n whereby n is the number of sides of the polygon. In our case n=8 because that an octagon, so us get:

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

Each exterior angle is the supplementary edge to the interior angle at the vertex of the polygon, for this reason in this situation each exterior edge is same to 45 degrees. (180 - 135 = 45). Remember the supplementary angles include up to 180 degrees. 

And due to the fact that there room 8 exterior angles, we multiply 45 levels * 8 and we gain 360 degrees.

This technique works because that every polygon, as long as you space asked to take it one exterior angle every vertex.

upvoted • 3 Downvote
comment • 5

blacksmith J.

Either ns don"t understand your thinking or you space talking bollocks. The inner angles add up tp 1080 in a polygon, in other words 135 each.

Jaycee D.

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

Jeanetto L.

I agree with the an initial person. That IS 135!!!

Emily M.

Its not correct the answer is 45, all you need to do it take 360 and also divide it by the number of sides (360/n) so lets say that the variety of sides is 6, her equation would certainly be 360/6 which would be and the answer would be 60. Check my mathematics if friend don"t think I"m right.

JAde W.

This aided me so much thank you 

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