document.write( "Question 1187046: At each vertex of a regular n-gon, the ratio of the interior angle to the exterior angle is 5:1. Find the value of n \n" ); document.write( "

Algebra.Com's Answer #817992 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "At each vertex of a regular n-gon, the ratio of the interior angle to the exterior angle is 5:1.
\n" ); document.write( "Find the value of n
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document.write( "Let x be the measure of the exterior angle;\r\n" );
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document.write( "then the measure of the interior angle is 5x, according to the condition.\r\n" );
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document.write( "Sp, we have\r\n" );
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document.write( "    x + 5x = 180  degrees,\r\n" );
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document.write( "     6x    = 180\r\n" );
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document.write( "      x    = 180/6 = 30.\r\n" );
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document.write( "Thus the exterior angle is 30 degrees, and the number of sides (= angles) of the regular n-gon is\r\n" );
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document.write( "      n =  = 12.     ANSWER\r\n" );
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