document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147506>Question 147506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The largest angle in a triangle is twice the degree measure of the second largest angle. One-third of the largest angle is 10 degrees larger than the difference of the other two. What is the measure in degrees of the smallest angle?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107885 by </B><A HREF=/tutors/aboutme.mpl?userid=aswathytony><B>aswathytony(47)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=aswathytony><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=107885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the angle measures  of the triangle be x, y ,z  where x is largest angle measure, y is second largest angle measure & z is smallest angle measure.\r<BR>\n" );
document.write( "\n" );
document.write( " given  largest angle is twice second largest angle i.e.  x = 2y  ..........(1)\r<BR>\n" );
document.write( "\n" );
document.write( "  one third of largest angle is  10 more than difference of other two<BR>\n" );
document.write( " <BR>\n" );
document.write( "i.e.  1/3 x =  (y - z) +10...........(2)\r<BR>\n" );
document.write( "\n" );
document.write( "    substituting (1) in (2)<BR>\n" );
document.write( "   <BR>\n" );
document.write( "   (1/3 )* 2y = (y - z) + 10 .<BR>\n" );
document.write( "  <BR>\n" );
document.write( "      2y/3 = y - z +10 \r<BR>\n" );
document.write( "\n" );
document.write( "      (2y/3) - y = - z + 10 \r<BR>\n" );
document.write( "\n" );
document.write( "     (2y - 3y) /3 = -z + 10 <BR>\n" );
document.write( "      -y  = -3z +30 <BR>\n" );
document.write( "    -y - 30 = -3z <BR>\n" );
document.write( "      y+30 = 3z <BR>\n" );
document.write( "      z =  (y+30) /3  ........(3)<BR>\n" );
document.write( "we know sum of angles of a triangle is 180deg\r<BR>\n" );
document.write( "\n" );
document.write( "i.e.     x + y+ z = 180 \r<BR>\n" );
document.write( "\n" );
document.write( "substituting (1) & (3) in above eq:\r<BR>\n" );
document.write( "\n" );
document.write( "         2y + y + (y + 30 )/3 = 180\r<BR>\n" );
document.write( "\n" );
document.write( "  6y + 3y + y + 30 = 180 * 3\r<BR>\n" );
document.write( "\n" );
document.write( "     10 y + 30 = 540<BR>\n" );
document.write( "         10y =  540 - 30 = 510 <BR>\n" );
document.write( "          y = 510 / 10 = 51.<BR>\n" );
document.write( "       x = 2y = 2 * 51 = 102 degrees\r<BR>\n" );
document.write( "\n" );
document.write( "         z = (y+30)/3  =( 51 + 30 )/3 =81/3 = 27 degrees.\r<BR>\n" );
document.write( "\n" );
document.write( "i.e measure of smallest angle is 27 degrees. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );