document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=651767>Question 651767</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the measures of the three angles of triangle ABC if the measure of angle A is equal to the measure of angle B. <BR>\n" );
document.write( "Measure of angle A: 2(6x-5y)+4<BR>\n" );
document.write( "Measure of angle B: 54-3(2x-3y)<BR>\n" );
document.write( "measure of angle C: 4(5x-6y)-2(4y-3x)+30 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407823 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=407823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the measure of angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+ ALIGN=MIDDLE  ALT=\"A+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is equal to the measure of angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then we have \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%286x-5y%29%2B4=54-3%282x-3y%29 ALIGN=MIDDLE  ALT=\"2%286x-5y%29%2B4=54-3%282x-3y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...we can solve this 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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x-10y%2B4=54-6x%2B9y ALIGN=MIDDLE  ALT=\"12x-10y%2B4=54-6x%2B9y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B6x=54%2B10y%2B9y-4 ALIGN=MIDDLE  ALT=\"12x%2B6x=54%2B10y%2B9y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18x=19y%2B50 ALIGN=MIDDLE  ALT=\"18x=19y%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=19y%2F18%2B50%2F18 ALIGN=MIDDLE  ALT=\"x=19y%2F18%2B50%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.06y%2B2.78 ALIGN=MIDDLE  ALT=\"x=1.06y%2B2.78\"   DISABLED_style= \"max-width:90%; height:auto;\" >....plug it in measure of angle C: \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%285%281.06y%2B2.78%29-6y%29-2%284y-3%281.06y%2B2.78%29%29%2B30 ALIGN=MIDDLE  ALT=\"4%285%281.06y%2B2.78%29-6y%29-2%284y-3%281.06y%2B2.78%29%29%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%285.3y%2B13.9-6y%29-2%284y-3.18y-8.34%29%2B30 ALIGN=MIDDLE  ALT=\"4%285.3y%2B13.9-6y%29-2%284y-3.18y-8.34%29%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21.2y%2B55.6-24y-8y%2B6.36y%2B16.68%2B30 ALIGN=MIDDLE  ALT=\"21.2y%2B55.6-24y-8y%2B6.36y%2B16.68%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "measure of angle C: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.44y%2B102.28 ALIGN=MIDDLE  ALT=\"-4.44y%2B102.28\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "now we have: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1.06y%2B2.78 ALIGN=MIDDLE  ALT=\"x=1.06y%2B2.78\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then\r<BR>\n" );
document.write( "\n" );
document.write( "the measure of angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2%286%281.06y%2B2.78%29-5y%29%2B4=2%286.36y%2B16.68-5y%29%2B4=2%281.36y%2B16.68%29%2B4=2.72y%2B33.36%2B4=2.72y%2B37.36 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+2.72y%2B37.36 ALIGN=MIDDLE  ALT=\"A=+2.72y%2B37.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "the measure of angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+ ALIGN=MIDDLE  ALT=\"B+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54-3%282.12y%2B5.56-3y%29 ALIGN=MIDDLE  ALT=\"54-3%282.12y%2B5.56-3y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54-3%28-0.88y%2B5.56%29 ALIGN=MIDDLE  ALT=\"54-3%28-0.88y%2B5.56%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54-%28-2.64y%2B16.68%29 ALIGN=MIDDLE  ALT=\"54-%28-2.64y%2B16.68%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54%2B2.64y-16.68 ALIGN=MIDDLE  ALT=\"54%2B2.64y-16.68\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.64y%2B37.32 ALIGN=MIDDLE  ALT=\"2.64y%2B37.32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=+2.64y%2B37.32 ALIGN=MIDDLE  ALT=\"B=+2.64y%2B37.32\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "the measure of angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=-4.44y%2B102.28 ALIGN=MIDDLE  ALT=\"C+=-4.44y%2B102.28\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "now in all measure of angles we have only one unknown variable, and we also know that  \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC=180 ALIGN=MIDDLE  ALT=\"A%2BB%2BC=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >...plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+ ALIGN=MIDDLE  ALT=\"A+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+ ALIGN=MIDDLE  ALT=\"B+\"   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;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282.72y%2B37.36%29%2B%282.64y%2B37.32%29%2B%28-4.44y%2B102.28%29=180 ALIGN=MIDDLE  ALT=\"%282.72y%2B37.36%29%2B%282.64y%2B37.32%29%2B%28-4.44y%2B102.28%29=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" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.72y%2B37.36%2B2.64y%2B37.32-4.44y%2B102.28=180 ALIGN=MIDDLE  ALT=\"2.72y%2B37.36%2B2.64y%2B37.32-4.44y%2B102.28=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.92y%2B176.96=180 ALIGN=MIDDLE  ALT=\"0.92y%2B176.96=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.92y=180-176.96 ALIGN=MIDDLE  ALT=\"0.92y=180-176.96\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.92y=3.04 ALIGN=MIDDLE  ALT=\"0.92y=3.04\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3.04%2F0.92 ALIGN=MIDDLE  ALT=\"y=3.04%2F0.92\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=3.3%29 ALIGN=MIDDLE  ALT=\"highlight%28y=3.3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "now find the measure of each angle:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+2.72y%2B37.36 ALIGN=MIDDLE  ALT=\"A=+2.72y%2B37.36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+2.72%2A3.3%2B37.36 ALIGN=MIDDLE  ALT=\"A=+2.72%2A3.3%2B37.36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+8.976%2B37.36 ALIGN=MIDDLE  ALT=\"A=+8.976%2B37.36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=+46.34%29 ALIGN=MIDDLE  ALT=\"highlight%28A=+46.34%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=+2.64%2A3.3%2B37.32 ALIGN=MIDDLE  ALT=\"B=+2.64%2A3.3%2B37.32\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=8.712%2B37.32 ALIGN=MIDDLE  ALT=\"B=8.712%2B37.32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28B=46.03%29 ALIGN=MIDDLE  ALT=\"highlight%28B=46.03%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=-4.44%2A3.3%2B102.28 ALIGN=MIDDLE  ALT=\"C+=-4.44%2A3.3%2B102.28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=-14.652%2B102.28 ALIGN=MIDDLE  ALT=\"C+=-14.652%2B102.28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C+=87.63%29 ALIGN=MIDDLE  ALT=\"highlight%28C+=87.63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "check:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC=180 ALIGN=MIDDLE  ALT=\"A%2BB%2BC=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=46.34%2B46.03%2B87.63=180 ALIGN=MIDDLE  ALT=\"46.34%2B46.03%2B87.63=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180=180 ALIGN=MIDDLE  ALT=\"180=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );