document.write( "Question 1012114: In a regular polygon, the exterior angle is one-eighth of an interior angle. How many sides has the polygon? \n" ); document.write( "

Algebra.Com's Answer #628007 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "In a regular polygon, the exterior angle is one-eighth of an interior angle. How many sides has the polygon?
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document.write( "First, let us find the interior angle.\r\n" );
document.write( "Let x be the exterior angle. Then the interior angle is 8x.\r\n" );
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document.write( "Their sum is 180°. It gives you an equation\r\n" );
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document.write( "x + 8x = 180,   or   9x = 180,   or x =  = 20°.\r\n" );
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document.write( "Thus the interior angle  =  =  = 160°.\r\n" );
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document.write( "Now use the formula for the sum of interior angles of n-sided regular polygon.\r\n" );
document.write( "It gives you an equation to determine n:\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( "n*160 = 180*(n-2).\r\n" );
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document.write( "Simplify and solve it:\r\n" );
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document.write( "160n = 180n - 360  ----->   20n = 360  ----->   n =  = 18.\r\n" );
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document.write( "Answer. n = 18.\r\n" );
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