document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=119555>Question 119555</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a quadrilateral JKLM, measure angle J=x,measure angle K=2x, measure angle L=2x+10,and measure angle M=3x-5. Find the measure of the angle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #87598 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=87598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For any quadrilateral, the sum of the 4 angles is 360 degrees. So in this case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J%2BK%2BL%2BM=360 ALIGN=MIDDLE  ALT=\"J%2BK%2BL%2BM=360\"   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=J%2BK%2BL%2BM=360 ALIGN=MIDDLE  ALT=\"J%2BK%2BL%2BM=360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2x%2B2x%2B10%2B3x-5=360 ALIGN=MIDDLE  ALT=\"x%2B2x%2B2x%2B10%2B3x-5=360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J=x ALIGN=MIDDLE  ALT=\"J=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=2x ALIGN=MIDDLE  ALT=\"K=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=2x%2B10 ALIGN=MIDDLE  ALT=\"L=2x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >,and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=3x-5 ALIGN=MIDDLE  ALT=\"M=3x-5\"   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=8x%2B5=360 ALIGN=MIDDLE  ALT=\"8x%2B5=360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x=360-5 ALIGN=MIDDLE  ALT=\"8x=360-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 5 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x=355 ALIGN=MIDDLE  ALT=\"8x=355\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28355%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x=%28355%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 8 to isolate x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=355%2F8 ALIGN=MIDDLE  ALT=\"x=355%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=355%2F8 ALIGN=MIDDLE  ALT=\"x=355%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=44.375 ALIGN=MIDDLE  ALT=\"x=44.375\"   DISABLED_style= \"max-width:90%; height:auto;\" > in decimal form), our first angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J=44.375 ALIGN=MIDDLE  ALT=\"J=44.375\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=44.375 ALIGN=MIDDLE  ALT=\"x=44.375\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can plug this into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=2x ALIGN=MIDDLE  ALT=\"K=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=2%2844.375%29=88.75 ALIGN=MIDDLE  ALT=\"K=2%2844.375%29=88.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our second angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=88.75 ALIGN=MIDDLE  ALT=\"K=88.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=44.375 ALIGN=MIDDLE  ALT=\"x=44.375\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can plug this into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=2x%2B10 ALIGN=MIDDLE  ALT=\"L=2x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=2%2844.375%29%2B10=88.75%2B10=98.75 ALIGN=MIDDLE  ALT=\"L=2%2844.375%29%2B10=88.75%2B10=98.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our third angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=98.75 ALIGN=MIDDLE  ALT=\"L=98.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=44.375 ALIGN=MIDDLE  ALT=\"x=44.375\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can plug this into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=3x-5 ALIGN=MIDDLE  ALT=\"M=3x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=3%2844.375%29-5=133.125-5=128.125 ALIGN=MIDDLE  ALT=\"M=3%2844.375%29-5=133.125-5=128.125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our fourth angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=128.125 ALIGN=MIDDLE  ALT=\"M=128.125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the measures of the four angles are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J=44.375 ALIGN=MIDDLE  ALT=\"J=44.375\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=88.75 ALIGN=MIDDLE  ALT=\"K=88.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=98.75 ALIGN=MIDDLE  ALT=\"L=98.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=128.125 ALIGN=MIDDLE  ALT=\"M=128.125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J%2BK%2BL%2BM=360 ALIGN=MIDDLE  ALT=\"J%2BK%2BL%2BM=360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44.375%2B88.75%2B98.75%2B128.125=360 ALIGN=MIDDLE  ALT=\"44.375%2B88.75%2B98.75%2B128.125=360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=J=44.375 ALIGN=MIDDLE  ALT=\"J=44.375\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=88.75 ALIGN=MIDDLE  ALT=\"K=88.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=98.75 ALIGN=MIDDLE  ALT=\"L=98.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=128.125 ALIGN=MIDDLE  ALT=\"M=128.125\"   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=360=360 ALIGN=MIDDLE  ALT=\"360=360\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add. Since the two sides of the equation are equal, this verifies our answer. </SPAN>\n" );
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