document.write( "Question 148008: In a regular polygon, the measure of each angle is 144 degree. How many sides does the polygon have? \n" ); document.write( "

Algebra.Com's Answer #108393 by Earlsdon(6294) $\"\"$ $\"About$

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In a regular polygon of n sides, the measure of each of the (equal) interior angles is given by:
\n" ); document.write( " $\"A%5Bi%5D+=+%28n-2%29180%2Fn\"$ Substitute $\"A%5Bi%5D+=+144\"$ and solve for n.
\n" ); document.write( " $\"144+=+%28n-2%29180%2Fn\"$ Multiply both sides by n and simplify.
\n" ); document.write( " $\"144n+=+180n-360\"$ Add 360 to both sides and subtract 144n from both sides.
\n" ); document.write( " $\"360+=+36n\"$ Divide both sides by 36.
\n" ); document.write( " $\"n+=+10\"$ A decagon. \n" ); document.write( "

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