SOLUTION: The sum of a regular polygon's angle measures is 1440 degrees. What is the measure of one of the angles of the regular polygon?

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Question 560370: The sum of a regular polygon's angle measures is 1440 degrees.
What is the measure of one of the angles of the regular polygon?

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The sum (S) of the interior angles of a polygon of n sides is given by:
S+=+%28n-2%29180 and S is given as 1440 so...
%28n-2%29180+=+1440 Divide both sides by 180.
n-2+=+8 Add 2 to both sides.
n+=+10 The regular polygon has 10 sides.
An interior angle (A) of a regular polygon of n sides is given by:
A+=+%28n-1%29180%2Fn But %28n-2%29180+=+1440 and n = 10:
A+=+1440%2F10
A+=+144degrees.