Algebra.Com's Answer #79589 by Edwin McCravy(20055)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Please help me answer or solve this question:
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document.write( "How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle?
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document.write( "It would be very helpful if you could explain the process that you took to solve this problem.
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document.write( "Thanks in advance,
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document.write( "Christine \r
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document.write( "The drawing below shows the bottom right-hand corner of the polygon:\r\n" );
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document.write( "The small acute angle marked x is an exterior angle of the\r\n" );
document.write( "polygon and the large obtuse angle marked 8x is an interior \r\n" );
document.write( "angle. It measures 8x because we are told that each interior \r\n" );
document.write( "angle is 8 times the measure of each exterior angle. \r\n" );
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document.write( "Since the interior and exterior angle at the same vertex\r\n" );
document.write( "of the polygon are supplementary, we can equate their sum to\r\n" );
document.write( "180°.\r\n" );
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document.write( "INTERIOR ANGLE + EXTERIOR ANGLE = 180°\r\n" );
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document.write( " 8x + x = 180°\r\n" );
document.write( " 9x = 180°\r\n" );
document.write( " x = 20°\r\n" );
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document.write( "This means each exterior angle is 20° and each interior\r\n" );
document.write( "angle is 180°-20° or 160°. This tells us that the polygon\r\n" );
document.write( "is a regular polygon because all the interior angles are\r\n" );
document.write( "equal in measure. \r\n" );
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document.write( "Now we only need to know that the theorem that says: \r\n" );
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document.write( "The sum of all the exterior angles of any polynomial is \r\n" );
document.write( "always 360°. \r\n" );
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document.write( "Let the number of sides of this polygon be N.\r\n" );
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document.write( "Since we know that this is an N-sided regular polygon, \r\n" );
document.write( "the sum of the exterior angles is N times 20° or 20N\r\n" );
document.write( "degrees. So \r\n" );
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document.write( " 20N degrees = 360 degrees\r\n" );
document.write( " 20N = 360\r\n" );
document.write( " N = 18 sides\r\n" );
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document.write( "So it is an 18-sided regular polygon. \r\n" );
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document.write( "Edwin \r
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