document.write( "Question 1107580: THE INTERIOR ANGLE ME A REGULAR CONVEX POLYGON IS 156 . HOW MANY SIDES HAS THE POLYGON? \n" ); document.write( "

Algebra.Com's Answer #722588 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "You can express the sum of all interior angle of any convex polygon with n sides (n vetices) as 180°*(n-2).\r\n" );
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document.write( "From the other side, the sum of all interior angle of any regular polygon is , where  is any of its interioir angle.\r\n" );
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document.write( "Thus you have this equation\r\n" );
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document.write( "180*(n-2) = n*156.\r\n" );
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document.write( "where n is unknown number of sides (of vertices).  Simplify and solve for n:\r\n" );
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document.write( "180n - 360 = 156n  ====>  180n - 156n = 360  ====>  24n = 360  ====>  n =  = 15.\r\n" );
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document.write( "Answer.  15 sides  and/or  15 verices.\r\n" );
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