document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127556>Question 127556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove the following statement:  If a triangle has one obtuse angle, then the other two angles are acute. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93480 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=93480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Use indirect reasoning to explain why a triangle cannot have more than one obtuse angle.\r<BR>\n" );
document.write( "\n" );
document.write( "First, assume that a triangle does have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=more+ ALIGN=MIDDLE  ALT=\"more+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=than+ ALIGN=MIDDLE  ALT=\"than+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=one+ ALIGN=MIDDLE  ALT=\"one+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=obtuse+ ALIGN=MIDDLE  ALT=\"obtuse+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=angle ALIGN=MIDDLE  ALT=\"angle\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "\n" );
document.write( "The measure of an obtuse angle is greater than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees. Hence, the sum of the measures of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=two+ ALIGN=MIDDLE  ALT=\"two+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=obtuse+ ALIGN=MIDDLE  ALT=\"obtuse+\"   DISABLED_style= \"max-width:90%; height:auto;\" >angles is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=greater ALIGN=MIDDLE  ALT=\"greater\"   DISABLED_style= \"max-width:90%; height:auto;\" > than <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, and the sum of the measures of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=three+ ALIGN=MIDDLE  ALT=\"three+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=obtuse ALIGN=MIDDLE  ALT=\"obtuse\"   DISABLED_style= \"max-width:90%; height:auto;\" > angles is greater that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=270 ALIGN=MIDDLE  ALT=\"270\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees. \r<BR>\n" );
document.write( "\n" );
document.write( "The sum of the angles of a triangle, however, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=equals+ ALIGN=MIDDLE  ALT=\"equals+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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" );
document.write( "\n" );
document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=only ALIGN=MIDDLE  ALT=\"only\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+one ALIGN=MIDDLE  ALT=\"+one\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+angle ALIGN=MIDDLE  ALT=\"+angle\"   DISABLED_style= \"max-width:90%; height:auto;\" > in a triangle can be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=obtuse ALIGN=MIDDLE  ALT=\"obtuse\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );