document.write( "Question 1203147: The sum of the interior angles of two regular polygons is 2520°. If the number of sides of one of the polygons is 3 less than twice the number of sides of the other, find the number of sides of each of the polygons. \n" ); document.write( "

Algebra.Com's Answer #838480 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "The sum of the interior angles of two regular polygons is 2520°.
\n" ); document.write( "If the number of sides of one of the polygons is 3 less than twice the number
\n" ); document.write( "of sides of the other, find the number of sides of each of the polygons.
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document.write( "Let n be the number of sides of the \"other\" polygon.\r\n" );
document.write( "Then the number of sides of the \"one\" polygon is (2n-3).\r\n" );
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document.write( "The sum of the interior angles of the \"other\" polygon is 180*(n-2) degrees.\r\n" );
document.write( "The sum of the interior angles of the \"one\"   polygon is 180*((2n-3)-2)) = 180*(2n-5) degrees.\r\n" );
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document.write( "The sum of the interior angles of both polygons is\r\n" );
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document.write( "    180*(n-2) + 180*(2n-5) = 2520.\r\n" );
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document.write( "Simplify and find n.  First divide the terms of the equation by 180\r\n" );
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document.write( "    (n-2) + (2n-5) = 2520/180 = 14\r\n" );
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document.write( "    3n - 7 = 14\r\n" );
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document.write( "    3n = 14 + 7 = 21\r\n" );
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document.write( "     n = 21/3 = 7.\r\n" );
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document.write( "ANSWER.  One polygon is a regular seven-sided polygon (septagon). \r\n" );
document.write( "         The other polygon is a regular 2*7-3 = 11-gon.\r\n" );
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