document.write( "Question 1151067: Can someone pls help with steps to answer the below question:\r
\n" ); document.write( "\n" ); document.write( "Name the polygon whose sum of the interior angle measures is twenty eight times the measure of one exterior angle of a regular octagon \n" ); document.write( "

Algebra.Com's Answer #772679 by ikleyn(52818) $\"\"$ $\"About$

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document.write( "Regular octagon is a regular 8-gon (8 vertices, 8 sides).\r\n" );
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document.write( "The exterior angle of the regular octagon is  360 degrees divided by 8, i.e.\r\n" );
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document.write( "     = 45 degrees.\r\n" );
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document.write( "Twenty eight times 45 degrees is  1260 degrees.\r\n" );
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document.write( "Thus the sum of interior angles of the polygon is  1260 degrees.\r\n" );
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document.write( "Using formula for the sum of the interior angles of a n-gon, you have this equation\r\n" );
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document.write( "    (n-2)*180 = 1260  degrees,   or\r\n" );
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document.write( "    n - 2 = 1260/180 = 7.\r\n" );
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document.write( "Hence,  n = 7+2 = 9, and the polygon is 9-gon (nonagon).     ANSWER\r\n" );
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