document.write( "Question 461249: What is the number of sides of a regular polygon if one angle measures 156° \n" ); document.write( "

Algebra.Com's Answer #316367 by Gogonati(855) $\"\"$ $\"About$

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The sum of the interior angles of a regular polygon with n angles is\r
\n" ); document.write( "\n" ); document.write( " $\"%28n-2%29180\"$ . Since the angle of our polygon measure 156 degree, then the sum \r
\n" ); document.write( "\n" ); document.write( "of interior angles is: $\"n%2A156\"$ . Equalizing these two expressions for the sum \r
\n" ); document.write( "\n" ); document.write( "of interior angles we have: $\"%28n-2%29%2A180=n%2A156\"$ , solving this equation we get:\r
\n" ); document.write( "\n" ); document.write( " $\"180n-156n=360\"$ => $\"24n=360\"$ => $\"n=15\"$ .\r
\n" ); document.write( "\n" ); document.write( "Answer:The number of sides of our polygon are 15. \n" ); document.write( "

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