document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002045>Question 1002045</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of x and y that will make each quadrilateral a parallelogram:\r<BR>\n" );
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document.write( "upper left angle: 3y degrees<BR>\n" );
document.write( "lower left angle: x degrees<BR>\n" );
document.write( "upper right angle: (4y-65) degrees<BR>\n" );
document.write( "lower right angle: 3y degrees </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #619066 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=619066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a parallelogram has opposite angles congruent.\r<BR>\n" );
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document.write( "upper left = lower right<BR>\n" );
document.write( "lower left = upper right\r<BR>\n" );
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document.write( "you are given that:\r<BR>\n" );
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document.write( "upper left angle: 3y degrees<BR>\n" );
document.write( "lower left angle: x degrees<BR>\n" );
document.write( "upper right angle: (4y-65) degrees<BR>\n" );
document.write( "lower right angle: 3y degrees\r<BR>\n" );
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document.write( "therefore:\r<BR>\n" );
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document.write( "3y = 3y<BR>\n" );
document.write( "x = 4y-65\r<BR>\n" );
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document.write( "a parallelogram has adjacent angles supplementary.\r<BR>\n" );
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document.write( "upper left + lower left = 180<BR>\n" );
document.write( "upper right + lower right = 180<BR>\n" );
document.write( "upper left + upper right = 180<BR>\n" );
document.write( "lower left + lower right = 180\r<BR>\n" );
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document.write( "therefore:\r<BR>\n" );
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document.write( "3y + x = 180<BR>\n" );
document.write( "4y - 65 + 3y = 180<BR>\n" );
document.write( "3y + 4y-65 = 180<BR>\n" );
document.write( "x + 3y = 180\r<BR>\n" );
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document.write( "from 3y + 4y - 65 = 180, you can solve for y to get:<BR>\n" );
document.write( "7y = 245<BR>\n" );
document.write( "y = 35\r<BR>\n" );
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document.write( "if y = 35, then 3y = 105 degrees.\r<BR>\n" );
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document.write( "3y is your upper left and lower right.\r<BR>\n" );
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document.write( "the other 2 angles must be supplementary to 105 which means they must be 75 degrees and must be congruent to each other.\r<BR>\n" );
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document.write( "those two angles are your lower left and upper right.\r<BR>\n" );
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document.write( "lower left equals x degrees, so x must be equal to 75.<BR>\n" );
document.write( "upper right equals 4y-65 degrees.<BR>\n" );
document.write( "since y = 35, 4y-65 = 140 - 65 = 75 degrees.\r<BR>\n" );
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document.write( "it all checks out.<BR>\n" );
document.write( "opposite angles are equal to each other.<BR>\n" );
document.write( "adjacent angles are supplementary to each other.\r<BR>\n" );
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document.write( "this occurs when:\r<BR>\n" );
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document.write( "y = 35<BR>\n" );
document.write( "x = 75\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "the value of your angles are shown below when y = 35 and x = 75\r<BR>\n" );
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document.write( "upper left angle: 3y degrees = 3*35 = 105<BR>\n" );
document.write( "lower left angle: x degrees = 75<BR>\n" );
document.write( "upper right angle: (4y-65) degrees = 4*5-65 = 140-65 = 75<BR>\n" );
document.write( "lower right angle: 3y degrees = 3*35 = 105\r<BR>\n" );
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document.write( " </SPAN>\n" );
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