document.write( "Question 1198819: Two sides of a regular n-gon, when extended meet at an angle 42 degrees. What is the least possible value of n? \n" ); document.write( "

Algebra.Com's Answer #832475 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "Two sides of a regular n-gon, when extended meet at an angle 42 degrees.
\n" ); document.write( "What is the least possible value of n?
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document.write( "The smallest angle between the sides of regular polygon is the exterior angle\r\n" );
document.write( "of the regular polygon, which is 360/n degrees.\r\n" );
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document.write( "Any angle between other sides of the regular polygon is a multiple of this \r\n" );
document.write( "minimal angle, i.e. is a multiple of 360/n degrees.\r\n" );
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document.write( "Thus to find the least possible value of n, we should select least possible \r\n" );
document.write( "value of n sich that 42 degrees is a multiple of 360/n.\r\n" );
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document.write( "Since 42 = 6*7 and 360 = 6*60, such least possible value of n  is 60.\r\n" );
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document.write( "Thus n = 60.\r\n" );
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document.write( "ANSWER.  n = 60.\r\n" );
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