document.write( "Question 589326: Hi I need you help solving a problem for a rhombus. The question asks to solve for the values of X and Y. I'm given a rhombus with angles labeled ABCD. ∠A is (4x-y) degrees ∠B is (2x-3y) degrees ∠C is (4x) degrees and ∠D is (2x-5y) degrees. There is also an exterior angle that extends from ∠D and that exterior angle is (6x+2y) degrees. Once again the question asks to solve for X and Y, and the shape if the figure is a rhombus. I hope this a good enough explanation that someone's able to help. Thank you. \n" ); document.write( "
Algebra.Com's Answer #374830 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Hi I need you help solving a problem for a rhombus. The question asks to solve for the values of x and y. I'm given a rhombus with angles labeled ABCD. ∠A is (4x-y) degrees ∠B is (2x-3y) degrees ∠C is (4x) degrees and ∠D is (2x-5y) degrees. There is also an exterior angle that extends from ∠D and that exterior angle is (6x+2y) degrees. Once again the question asks to solve for X and Y, and the shape if the figure is a rhombus. I hope this a good enough explanation that someone's able to help. Thank you.
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document.write( "Opposite angles of a rhombus have equal measures, so\r\n" );
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document.write( "             m∠A = m∠C\r\n" );
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document.write( "            4x-y = 4x\r\n" );
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document.write( "             m∠B = m∠ADC\r\n" );
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document.write( "           2x-3y = 2x-5y\r\n" );
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document.write( "The two angles at D are supplementary, so\r\n" );
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document.write( "  m∠ADE + m∠ADC = 180°\r\n" );
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document.write( "(6x+2y) + (2x-5y) = 180\r\n" );
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document.write( "(1)              4x-y = 4x\r\n" );
document.write( "(2)             2x-3y = 2x-5y\r\n" );
document.write( "(3)   6x+2y + (2x-5y) = 180\r\n" );
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document.write( "Simplifying equation (1)\r\n" );
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document.write( "(1)              4x-y = 4x\r\n" );
document.write( "                   -y = 0\r\n" );
document.write( "                    y = 0\r\n" );
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document.write( "Substituting y = 0 in (2) and (3)\r\n" );
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document.write( "(2)             2x-3·0 = 2x-5·0\r\n" );
document.write( "(3)   6x+2·0 + (2x-5·0) = 180\r\n" );
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document.write( "(2)                  2x = 2x\r\n" );
document.write( "(3)           6x + (2x) = 180\r\n" );
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document.write( "Solving (3)\r\n" );
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document.write( "                    8x = 180\r\n" );
document.write( "                     x = 22.5°\r\n" );
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document.write( "So the rhombus is really a square.\r\n" );
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document.write( "Edwin
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