SOLUTION: What is the measure of each exterior angle of a regular 72-gon?

Question 1147469: What is the measure of each exterior angle of a regular 72-gon?
Found 2 solutions by greenestamps, 750033275:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The sum of the measures of all the exterior angles of any convex polygon is 360 degrees.

If the polygon is regular and has n sides, the measure of each exterior angle is 360/n degrees.

Do the arithmetic for n=72....
Answer by 750033275(2) (Show Source): You can put this solution on YOUR website!
To find the measure of an exterior angle of a polygon, use these formula in this order.

In this case, s is the sum of the interior-angle measurements of the polygon, and e is the measure of an exterior angle of the polygon.
Let n be 72.
Then, solve (72 - 2).
72 - 2 = 70
Next, multiply the difference by 180.
70 * 180 = 12,600
Now, divide the product by 72.
12,600 ÷ 72 = 175
Finally, subtract the quotient from 180.
180 - 175 = 5
So, the measure of each exterior angle of a regular 72-gon is 5°.
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