A preeminence of polygons is the the amount of the exterior angles constantly equals 360 degrees, however lets prove this for a continual octagon (8-sides).

You are watching: Find the sum of the measures of exterior angles one at each vertex of an octagon

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

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

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

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

And since there room 8 exterior angles, we multiply 45 levels * 8 and we acquire 360 degrees.

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

upvote • 3 Downvote
comments • 5

smith J.

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

Jaycee D.

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

Jeanetto L.

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

Emily M.

Its wrong the prize is 45, every you have to do it take it 360 and divide that by the number of sides (360/n) so lets say the the variety of sides is 6, her equation would certainly be 360/6 which would be and also the answer would certainly be 60. Inspect my mathematics if you don"t think I"m right.

JAde W.

This aided me so much thank you 

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