SOLUTION: In a regular polygon, the measure of each angle is 144 degree. How many sides does the polygon have?

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Question 148008: In a regular polygon, the measure of each angle is 144 degree. How many sides does the polygon have?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
In a regular polygon of n sides, the measure of each of the (equal) interior angles is given by:
A%5Bi%5D+=+%28n-2%29180%2Fn Substitute A%5Bi%5D+=+144 and solve for n.
144+=+%28n-2%29180%2Fn Multiply both sides by n and simplify.
144n+=+180n-360 Add 360 to both sides and subtract 144n from both sides.
360+=+36n Divide both sides by 36.
n+=+10 A decagon.