document.write( "Question 1021212: Please help me solve this question: Four angles of a pentagon are equal and the fifth is 60°. Find the angles and show that two sides of the pentagon are parallel. Thank you \n" ); document.write( "
Algebra.Com's Answer #638010 by Edwin McCravy(20060)\"\" \"About 
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document.write( "The pentagon ABCDE above is given to be drawn such that\r\n" );
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document.write( "∠A = 60°, and ∠B = ∠C = ∠D = ∠E \r\n" );
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document.write( "The sum of the interior angles of a polygon of n sides\r\n" );
document.write( "is given by the formula:\r\n" );
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document.write( "   (n-2)∙180°\r\n" );
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document.write( "The pentagon above has 5 sides, so n=5.  Substituting n=5,\r\n" );
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document.write( "   (5-2)∙180° =\r\n" );
document.write( "     (3)∙180° =\r\n" );
document.write( "         540°\r\n" );
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document.write( "So  ∠A + ∠B + ∠C + ∠D + ∠E = 540°\r\n" );
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document.write( "Suppose ∠A = 60° and all the other angles = x°\r\n" );
document.write( "then:\r\n" );
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document.write( "    60° + x° + x° + x° + x° = 540°\r\n" );
document.write( "                  60° + 4x° = 540°\r\n" );
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document.write( "Subtract 60° from both sides:\r\n" );
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document.write( "                        4x° = 480°\r\n" );
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document.write( "Divide both sides by 4\r\n" );
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document.write( "                         x° = 120°\r\n" );
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document.write( "So in the figure above,\r\n" );
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document.write( "∠A = 60°,  ∠B = ∠C = ∠D = ∠E = 120° \r\n" );
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document.write( "Now we recall a well-known theorem of geometry:\r\n" );
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document.write( "When a transversal intersects two lines, the two \r\n" );
document.write( "lines are parallel if and only if interior angles \r\n" );
document.write( "on the same side of the transversal are \r\n" );
document.write( "supplementary (sum to 180°).\r\n" );
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document.write( "∠A and ∠B are supplementary because ∠A + ∠B = 60° + 120° = 180°\r\n" );
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document.write( "Lines AE and BC are two lines cut by transversal AB.\r\n" );
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document.write( "Therefore by the theorem, AE ∥ BC.\r\n" );
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document.write( "Similarly,\r\n" );
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document.write( "∠A and ∠E are supplementary because ∠A + ∠E = 60° + 120° = 180°\r\n" );
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document.write( "Lines AB and EC are two lines cut by transversal AE.\r\n" );
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document.write( "Therefore by the theorem, AB ∥ EC.\r\n" );
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document.write( "Edwin
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