document.write( "Question 1150931: the ratio of the interior angles and exterior angles of a regular n-gon (n sided polygon) to the exterior angles is 10 to 2,
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Algebra.Com's Answer #772501 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "You are given that the ratio of the interior angle of the regular n-gon to its exterior angle is 10:2, i.e, 5:1.\r\n" );
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document.write( "From the other side, the sum of these angles is 180 degrees, as you should know.\r\n" );
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document.write( "Hence, the exterior angle is   =  = 30 degrees.\r\n" );
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document.write( "Then the interior angle is  180-30 = 150 degrees, obviously.\r\n" );
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document.write( "From the other side, the sum of the exterior angles of any n-sided convex polygon is 360 degrees.\r\n" );
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document.write( "It gives you an equation\r\n" );
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document.write( "    n*30 = 360  degrees\r\n" );
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document.write( "to find the number of sides / (of vertices) of the polygon.\r\n" );
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document.write( "From the equation, you easily find  n =  = 12.\r\n" );
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document.write( "ANSWER.  The given polygon is 12-gon.\r\n" );
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