document.write( "Question 1044690: Is it possible to have a regular polygon each of whose exterior angel is 50 ? \n" ); document.write( "
Algebra.Com's Answer #660024 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
No, and here's why.  It's because: \r\n" );
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document.write( "1. There are n exterior angles of any n-sided polygon.\r\n" );
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document.write( "2. All the exterior angles of any polygon have sum 360°.\r\n" );
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document.write( "3. All exterior angles of a REGULAR polygon are congruent, i.e.,\r\n" );
document.write( "   their measures are all equal.\r\n" );
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document.write( "4.  Therefore each exterior angle of an n-sided polygon is 360°/n.\r\n" );
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document.write( "5.  So therefore if it were possible to have such a regular polygon, \r\n" );
document.write( "    then each of its exterior angles would be 50°.\r\n" );
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document.write( "6. That would mean that 360°/n = 50°\r\n" );
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document.write( "7.  When we solve 360°/n = 50° for n we get:\r\n" );
document.write( "                    360° = 50°n\r\n" );
document.write( "                360°/50° = n\r\n" );
document.write( "                  360/50 = n\r\n" );
document.write( "                    36/5 = n\r\n" );
document.write( "                   7 1/5 = n\r\n" );
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document.write( "8.  No polygon, regular or not, can have 7 and 1/5th sides.  \r\n" );
document.write( "    The number of sides is always a counting number, a positive\r\n" );
document.write( "    whole number or integer.\r\n" );
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document.write( "Edwin
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