document.write( "Question 824378: Two alternate sides of a regular polygon,when produced,meet at the right angle. calculate the number of sides in the polygon.\r
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Algebra.Com's Answer #496412 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Let's sketch a few sides of the regular polygon and extend\r\n" );
document.write( "two alternate sides until they meet at a right angle ∠C.\r\n" );
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document.write( "Suppose the regular polygon has n sides.\r\n" );
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document.write( "∠DAB ≅ ∠EBA because interior angles of \r\n" );
document.write( "a regular polygon are congruent.\r\n" );
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document.write( "∠CAB ≅ ∠CBA  because they are supplements of\r\n" );
document.write( "congruent angles\r\n" );
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document.write( "∠ACB is a right angle because it is given that\r\n" );
document.write( "the extensions of DA and EB form a right angle.\r\n" );
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document.write( "ΔABC is an isosceles right triangle.\r\n" );
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document.write( "m∠CAB = m∠CBA = 45° because they are base angles\r\n" );
document.write( "of an isosceles right triangle. \r\n" );
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document.write( "∠CAB, which has measure 45°, is an exterior angle of the polygon.\r\n" );
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document.write( "The sum of all n exterior angles of any polygon is 360°\r\n" );
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document.write( "All n exterior angles of a regular polygon are congruent.\r\n" );
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document.write( "Therefore \r\n" );
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document.write( "n×45° = 360°\r\n" );
document.write( "    n = \"%22360%B0%22%2F%2245%B0%22\"\r\n" );
document.write( "    n = 8\r\n" );
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document.write( "So the regular polygon has 8 sides.  It is a regular octagon:\r\n" );
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document.write( "Edwin
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