document.write( "Question 1150365: The sum of interior angles of a regular polygon is 24 times the size of the exterior angle.
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Algebra.Com's Answer #771746 by ikleyn(52908) $\"\"$ $\"About$

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document.write( "The problem says\r\n" );
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document.write( "    180*(n-2) = 24*(360/n).     (1)\r\n" );
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document.write( "Here \"n\" is the number of sides (vertices)  of the polygon;\r\n" );
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document.write( "left side is the sum of interior angles;  right side is 24 times the exterior angle.\r\n" );
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document.write( "Simplify equation (1). First step is to cancel the factor 180 in both sides.\r\n" );
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document.write( "    n-2 = 24*(2/n)\r\n" );
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document.write( "    n^2 - 2n = 48\r\n" );
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document.write( "    n^2 - 2n - 48 = 0\r\n" );
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document.write( "    (n-8)*(n+6) = 0.\r\n" );
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document.write( "Of the two roots, only positive root  n= 8 makes sense.\r\n" );
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document.write( "ANSWER. Number of sides is 8.  The polygon is a regular octagon.\r\n" );
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