document.write( "Question 1122224: If the sum of all the angles except one of a convex polygon is 2190 degrees then the number of sides must be?
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Algebra.Com's Answer #738302 by ikleyn(52810) $\"\"$ $\"About$

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document.write( "The sum of all interior angles of an n-sided polygon is  180°*(n-2).\r\n" );
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document.write( "The table below represents the sums of all interior angles of n-sided polygons for 3 <= n <= 16.\r\n" );
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document.write( "    Table\r\n" );
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document.write( "n     Sum of all interior angles\r\n" );
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document.write( "3	180\r\n" );
document.write( "4	360\r\n" );
document.write( "5	540\r\n" );
document.write( "6	720\r\n" );
document.write( "7	900\r\n" );
document.write( "8	1080\r\n" );
document.write( "9	1260\r\n" );
document.write( "10	1440\r\n" );
document.write( "11	1620\r\n" );
document.write( "12	1800\r\n" );
document.write( "13	1980\r\n" );
document.write( "14	2160\r\n" );
document.write( "15	2340\r\n" );
document.write( "16	2520\r\n" );
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document.write( "From the table, you easily can conclude that your polygon must have n > 14 and n <= 15 sides.   \r\n" );
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document.write( "    (It is so because the missed interior angle of a convex polygon is less than 180°).\r\n" );
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document.write( "Hence, n = 15.\r\n" );
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