document.write( "Question 2279: Is it possible to have a regular polygon with interior angles measuring 15 degrees? If so how many sides does it have? \n" ); document.write( "

Algebra.Com's Answer #960 by longjonsilver(2297) $\"\"$ $\"About$

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the sum of the interior angles of a polygon are:\r
\n" ); document.write( "\n" ); document.write( "3 sides = 1*180
\n" ); document.write( "4 sides = 2*180
\n" ); document.write( "5 sides = 3*180
\n" ); document.write( "6 sides = 4*180
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\n" ); document.write( "13 sides = 11*180\r
\n" ); document.write( "\n" ); document.write( "see a pattern?\r
\n" ); document.write( "\n" ); document.write( "n sides = (n-2)*180\r
\n" ); document.write( "\n" ); document.write( "So for a regular polygon, each angle would be this divided the number of sides. And can this be 15?\r
\n" ); document.write( "\n" ); document.write( "so $\"180%28n-2%29%2Fn+=+15\"$
\n" ); document.write( "180n - 360 = 15n
\n" ); document.write( "165n = 360
\n" ); document.write( "n = 2.1818\r
\n" ); document.write( "\n" ); document.write( "so it is NOT possible, since this is not a whole number (remember n is the number of sides).\r
\n" ); document.write( "\n" ); document.write( "jon \n" ); document.write( "

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