SOLUTION: How do I solve the equation to find out how many sides a regular polygon has if the interior angle is 144 degrees?

Algebra ->  Polygons -> SOLUTION: How do I solve the equation to find out how many sides a regular polygon has if the interior angle is 144 degrees?       Log On


   

Question 224560: How do I solve the equation to find out how many sides a regular polygon has if the interior angle is 144 degrees?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of an interior angle A%5Bi%5D of a regular polygon of n sides is given by:
A%5Bi%5D+=+%28n-2%29%28180%29%2Fn Substitute A%5Bi%5D+=+144
144+=+%28n-2%29%28180%29%2Fn Multiply both sides by n.
144n+=+%28n-2%29%28180%29 Simplify the right side.
144n+=+180n-360 Add 360 to both sides.
360%2B144n+=+180n Subtract 144n from both sides.
360+=+36n Divide both sides by 36.
10+=+n
The number of side is 10. This is called a "decagon"