document.write( "Question 450813: If the sum of the interior angles of a polygon is 1800° where one of the interior angles measures 172° and all others are congruent, how many sides
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Algebra.Com's Answer #310098 by Edwin McCravy(20055)\"\" \"About 
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document.write( "The formula for the sum of the interior angles\r\n" );
document.write( "of a polygon with n sides is\r\n" );
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document.write( "(n - 2)180°\r\n" );
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document.write( "We set that equal to 1800°\r\n" );
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document.write( "(n - 2)180° = 1800°\r\n" );
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document.write( "Divide both sides by 180°\r\n" );
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document.write( "n - 2 = 10\r\n" );
document.write( "    n = 12\r\n" );
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document.write( "So the polygon has 12 sides, and therefore\r\n" );
document.write( "12 interior angles.\r\n" );
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document.write( "Since one of the angles is 172°,\r\n" );
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document.write( "the other 11 interior angles must have sum\r\n" );
document.write( "1800°-172°=1628°\r\n" );
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document.write( "Since they are all congruent, we divide 1628°/11 = 148°.\r\n" );
document.write( "So each of the other 11 interior angles measures 148°.\r\n" );
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document.write( "So it's a 12-sided polygon.  I'll draw it with the 172°\r\n" );
document.write( "angle at the top.  172° is close to 180°, so it looks almost\r\n" );
document.write( "like the the two sides at the top form a straight line,\r\n" );
document.write( "but they don't.  I'll color the sides of the 172° angle red\r\n" );
document.write( "and green, so it will look like a 12-sided polygon, not\r\n" );
document.write( "a 11-sided one. Here's what it looks like:\r\n" );
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document.write( "Edwin
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