document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129631>Question 1129631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two consecutive angles of a parallelogram are in the ratio 4:5.How many degrees are there in each angle of the parallelogram? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746209 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=746209\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "by definition, the sum of the angles for each quadrilateral is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360 ALIGN=MIDDLE  ALT=\"360\"   DISABLED_style= \"max-width:90%; height:auto;\" >°<BR>\n" );
document.write( "the sum of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=two ALIGN=MIDDLE  ALT=\"two\"   DISABLED_style= \"max-width:90%; height:auto;\" > consecutive angles of a parallelogram have to be equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180 ALIGN=MIDDLE  ALT=\"180\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees\r<BR>\n" );
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document.write( "let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = one of the angles and let<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y ALIGN=MIDDLE  ALT=\"+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the other angle.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+180 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the ratio of one of these angles to the other is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fy+=+4%2F5 ALIGN=MIDDLE  ALT=\"x%2Fy+=+4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%284%2F5%29+y ALIGN=MIDDLE  ALT=\"x+=+%284%2F5%29+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+180 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F5%29+y+%2B+y+=+180 ALIGN=MIDDLE  ALT=\"%284%2F5%29+y+%2B+y+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F5%29+y+%2B%285%2F5%29+y+=+180 ALIGN=MIDDLE  ALT=\"%284%2F5%29+y+%2B%285%2F5%29+y+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F5%29+y+=+180 ALIGN=MIDDLE  ALT=\"%289%2F5%29+y+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+180%2F%289%2F5%29 ALIGN=MIDDLE  ALT=\"+y+=+180%2F%289%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28180%2A5%29%2F9 ALIGN=MIDDLE  ALT=\"+y+=+%28180%2A5%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28cross%28180%2920%2A5%29%2Fcross%289%29 ALIGN=MIDDLE  ALT=\"+y+=+%28cross%28180%2920%2A5%29%2Fcross%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+100 ALIGN=MIDDLE  ALT=\"+y+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+100+=+180 ALIGN=MIDDLE  ALT=\"x+%2B+100+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=80 ALIGN=MIDDLE  ALT=\"x=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the sum of two consecutive angles is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100+%2B+80+=+180 ALIGN=MIDDLE  ALT=\"100+%2B+80+=+180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "check the ratio:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2F100=4%2F5 ALIGN=MIDDLE  ALT=\"80%2F100=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F10=4%2F5 ALIGN=MIDDLE  ALT=\"8%2F10=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> proves that angles of a parallelogram are in the ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%3A5 ALIGN=MIDDLE  ALT=\"4%3A5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );