Question

what is the sum of the measures of the exterior angles of a decagon? please help and explain

Answer 1

What is a decagon?

Answer 2

a polygon with 10sides and 10 angles

Answer 3

Is it a regular decagon?

Answer 4

should be. I don't know, im not the one posted this

Answer 5

http://www.mathopenref.com/decagon.html

Answer 6

Basically, the sum of the angles inside an n-sided polygon is 180*(n-2)

Answer 7

a regular polygon*

Answer 8

not interior, exterior is what i need

Answer 9

so each angle in the decagon is 144 degrees.

To find the measure of each exterior angle, we take advantage of the fact that the sum of the interior and the exterior angle is 180

so the measure of each exterior angle is 180 - 144 = 36 degrees

multiply that by 10 to get the sum of the measures of the exterior angles of a regular decagon, which is 360

Answer 10

for a regular polygon with n sides, each interior angle is\[\frac{180(n-2)}{n}=180-\frac{360}{n}\]degrees.

each exterior angle is \[180 - (180-\frac{360}{n})=\frac{360}{n}\]multiply by n to get the sum of the measures of the exterior angles of the n-sides polygon\[360\]
therefore, for any n-sided regular polygon, the sum of the measures of the exterior angles will always be equal to 360