document.write( "Question 578709: In a convex n-gon, the sum of all angles except one angle is 2270 . find the number of sides of n-gon . \n" ); document.write( "
Algebra.Com's Answer #370732 by Edwin McCravy(20055)\"\" \"About 
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document.write( "Let the number of sides be n and the angle not included in the\r\n" );
document.write( "sum of 2270° have measure k°.\r\n" );
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document.write( "Then:\r\n" );
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document.write( " (n-1)180° = 2270° + k°  \r\n" );
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document.write( "180n - 180 = 2270 + k\r\n" );
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document.write( "      180n = 2450 + k\r\n" );
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document.write( "         n = \"%282450+%2B+k%29%2F180\"\r\n" );
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document.write( "Since n must be a positive integer, 2450 + k must be a multiple of 180.\r\n" );
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document.write( "The smallest multiple of 180 greater than 2450 is 2520 or 14*180 which would \r\n" );
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document.write( "make k = 2520-2450 or 70.  Thus n=14 (with the omitted angle 70°) is a \r\n" );
document.write( "solution.\r\n" );
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document.write( "The next multiple of 180°, 2700 or 15×180 would cause k° to be 250° which\r\n" );
document.write( "would give us a concave polygon.  But we are given that the polygon is\r\n" );
document.write( "convex, i.e., all interior angles are less than 180°.\r\n" );
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document.write( "Therefore there is just one solution, a polygon of 14 sides.\r\n" );
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document.write( "Edwin
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