document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037714>Question 1037714</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If c=14x° & A=(3x+10)° what is the value of x in the isosceles trapezoid? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652511 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=652511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An isosceles trapezoid looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C250%2C-1%2C8%2C-1%2C6.5%2C%0D%0Aline%280%2C0%2C7%2C0%29%2Cline%282%2C5.5%2C5%2C5.5%29%2C%0D%0Aline%280%2C0%2C2%2C5.5%29%2Cline%287%2C0%2C5%2C5.5%29%2C%0D%0Agreen%28arc%280%2C0%2C2%2C2%2C-70%2C0%29%29%2Cgreen%28arc%287%2C0%2C2%2C2%2C-180%2C-110%29%29%2C%0D%0Ared%28arc%282%2C5.5%2C2%2C2%2C0%2C110%29%29%2Cred%28arc%282%2C5.5%2C1.5%2C1.5%2C0%2C110%29%29%2C%0D%0Ared%28arc%285%2C5.5%2C2%2C2%2C70%2C180%29%29%2Cred%28arc%285%2C5.5%2C1.5%2C1.5%2C70%2C180%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , with two congruent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28acute%29 ALIGN=MIDDLE  ALT=\"green%28acute%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > angles and two congruent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28obtuse%29 ALIGN=MIDDLE  ALT=\"red%28obtuse%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > angles.<BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28acute%29 ALIGN=MIDDLE  ALT=\"green%28acute%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > angles are supplementary to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28obtuse%29 ALIGN=MIDDLE  ALT=\"red%28obtuse%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > angles.<BR>\n" );
document.write( "The vertices in a trapezoid (or any polygon) are named going around in order (clockwise or counterclockwise).<BR>\n" );
document.write( "No matter how the vertices in your isosceles trapezoid are named,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" >angles are opposite vertices/angles.<BR>\n" );
document.write( "The opposite angles in an isosceles trapezoid<BR>\n" );
document.write( "(one acute and one obtuse) are supplementary,<BR>\n" );
document.write( "meaning that their measures add up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180%5Eo ALIGN=MIDDLE  ALT=\"180%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BC=180%5E0 ALIGN=MIDDLE  ALT=\"A%2BC=180%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , meaning that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x%2B%283x%2B10%29=180 ALIGN=MIDDLE  ALT=\"14x%2B%283x%2B10%29=180\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Now, all you have to do is solve that equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14x%2B%283x%2B10%29=180 ALIGN=MIDDLE  ALT=\"14x%2B%283x%2B10%29=180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2814x%2B3x%29%2B10=180 ALIGN=MIDDLE  ALT=\"%2814x%2B3x%29%2B10=180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17x%2B10=180 ALIGN=MIDDLE  ALT=\"17x%2B10=180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17x=180-10 ALIGN=MIDDLE  ALT=\"17x=180-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17x=170 ALIGN=MIDDLE  ALT=\"17x=170\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=170%2F17 ALIGN=MIDDLE  ALT=\"x=170%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=10%29 ALIGN=MIDDLE  ALT=\"highlight%28x=10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "If we are curious, we can figure out the measures of the angles as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=14x%5Eo=14%2A%2810%5Eo%29=140%5Eo ALIGN=MIDDLE  ALT=\"C=14x%5Eo=14%2A%2810%5Eo%29=140%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%283x%2B10%29%5Eo=%283%2A10%2B10%29%5Eo=%2830%2B10%29%5Eo=40%5Eo ALIGN=MIDDLE  ALT=\"A=%283x%2B10%29%5Eo=%283%2A10%2B10%29%5Eo=%2830%2B10%29%5Eo=40%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, the isosceles trapezoid in the problem looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28800%2C250%2C-0.5%2C7.5%2C-0.5%2C2%2C%0D%0Aline%280%2C0%2C7%2C0%29%2Cline%282%2C1.68%2C5%2C1.68%29%2C%0D%0Aline%280%2C0%2C2%2C1.68%29%2Cline%287%2C0%2C5%2C1.68%29%2C%0D%0Agreen%28arc%280%2C0%2C1.3%2C1.3%2C-40%2C0%29%29%2Cgreen%28arc%287%2C0%2C1.3%2C1.3%2C-180%2C-140%29%29%2C%0D%0Ared%28arc%282%2C1.68%2C1%2C1%2C0%2C140%29%29%2Cred%28arc%282%2C1.68%2C0.75%2C0.75%2C0%2C140%29%29%2C%0D%0Ared%28arc%285%2C1.68%2C1%2C1%2C40%2C180%29%29%2Cred%28arc%285%2C1.68%2C0.75%2C0.75%2C40%2C180%29%29%2C%0D%0Alocate%282%2C1.68%2Cred%28140%5Eo%29%29%2Clocate%280.3%2C0.3%2Cgreen%2840%5Eo%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "A rectangle is considered a special case of a trapezoid,<BR>\n" );
document.write( "and it can be considered an isosceles trapezoid.<BR>\n" );
document.write( "In that case, all four angles would measure <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90%5Eo ALIGN=MIDDLE  ALT=\"90%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "with no acute or obtuse angle,<BR>\n" );
document.write( "but opposite angles would still be supplementary.<BR>\n" );
document.write( "That is not the case with the problem above,<BR>\n" );
document.write( "but the reasoning above would have worked just the same,<BR>\n" );
document.write( "even if we had figured out that both angles were right angles. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );