document.write( "Question 135203: the sum of the measures of the interior angles of a polygon is between 2100 and 2400. how many sides does the polygon have? thanks..
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Algebra.Com's Answer #99089 by Edwin McCravy(20062)\"\" \"About 
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the sum of the measures of the interior angles of a polygon is between 2100 and 2400. how many sides does the polygon have? thanks.
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document.write( "The expression for the sum of the interior angles of\r\n" );
document.write( "an \"n\"-sided polygon is:\r\n" );
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document.write( "\"%28n-2%29180\"°\r\n" );
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document.write( "\"2100+%3C=+%28n-2%29180%3C=2400\"\r\n" );
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document.write( "Divide all three sides by \"60\"\r\n" );
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document.write( "\"2100%2F60+%3C=+%28%28n-2%29180%29%2F60%3C=2400%2F60\"\r\n" );
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document.write( "\"35+%3C=+%28n-2%293%3C=40\"\r\n" );
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document.write( "\"35+%3C=+3%28n-2%29%3C=40\"\r\n" );
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document.write( "\"35+%3C=+3n-6%3C=40\"\r\n" );
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document.write( "Add \"6\" to all three sides:\r\n" );
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document.write( "\"41+%3C=+3n%3C=46\"\r\n" );
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document.write( "Divide all three sides by \"3\"\r\n" );
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document.write( "\"41%2F3+%3C=+%283n%29%2F3%3C=46%2F3\"\r\n" );
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document.write( "\"13\"\"2%2F3+%3C=+n+%3C=+15\"\"1%2F3\"\r\n" );
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document.write( "\"n\" must be an integer and the only\r\n" );
document.write( "two integers between \"13\"\"2%2F3\" and \"15\"\"1%2F3\"\r\n" );
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document.write( "are \"14\" and \"15\".\r\n" );
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document.write( "So the polygon could either\r\n" );
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document.write( "1. have \"14\" sides, with the sum of the interior angles being\r\n" );
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document.write( "\"%28n-2%29180\"°\r\n" );
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document.write( "\"%2814-2%29180\"°\r\n" );
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document.write( "\"%2812%29180\"°\r\n" );
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document.write( "\"2160\"°\r\n" );
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document.write( "OR\r\n" );
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document.write( "2. have \"15\" sides, with the sum of the interior angles being\r\n" );
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document.write( "\"%28n-2%29180\"°\r\n" );
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document.write( "\"%2815-2%29180\"°\r\n" );
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document.write( "\"%2813%29180\"°\r\n" );
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document.write( "\"2340\"°\r\n" );
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document.write( "So there are two solutions.  The number of sides is \"14\" or \"15\".\r\n" );
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document.write( "Edwin
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