document.write( "Question 1011166: A regular polygon's interior angle is 8 times as large as its exterior angle \n" ); document.write( "

Algebra.Com's Answer #626753 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A regular polygon's interior angle is 8 times as large as its exterior angle
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\n" ); document.write( "\n" ); document.write( "Hello,\r
\n" ); document.write( "\n" ); document.write( "your posting is not complete! A question is absent.\r
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\n" ); document.write( "\n" ); document.write( "The question is: Find the number of sides of the polygon.
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document.write( "First let us find the interior angle . \r\n" );
document.write( "According to the condition, \r\n" );
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document.write( "  +  = 180°.\r\n" );
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document.write( "Hence,  +  = 180°*8,  or   = 180°*8,  or   =  = 20°*8 = 160°.\r\n" );
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document.write( "Now find n, the number of sides, from the equation\r\n" );
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document.write( " = 160,  or\r\n" );
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document.write( "(n-2)*180 = n*160  -----> (n-2)*9 = n*8,  -----> 9n - 18 = 8n  -----> 9n - 8n = 18  -----> n = 18.\r\n" );
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document.write( "Answer. The number of sides of the regular polygon is 18.\r\n" );
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