document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173993>Question 173993</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a hexagon three angles have the same measure. The measure of each of the congruent angles is twice the measure of the fourth angle and is half the measure of the fifth angle. The sixth angle measures 115. What is the measure 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 #128905 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=128905\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a hexagon has 6 angles.<BR>\n" );
document.write( "the total number of internal degrees is (n-2)*180 = 4*180 = 720 degrees.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let a = one of the congruent angles.<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "angles 1, 2, and 3 = a.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if a = 2 * angle 4, then angle 4 = 1/2 * a<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if a = 1/2 * angle 5, then angle 5 = 2 * a<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we have:<BR>\n" );
document.write( "angle 1 = a<BR>\n" );
document.write( "angle 2 = a<BR>\n" );
document.write( "angle 3 = a<BR>\n" );
document.write( "angle 4 = 1/2 * a<BR>\n" );
document.write( "angle 5 = 2 * a<BR>\n" );
document.write( "angle 6 = 115<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the sum of the angles is equal to 720, we have:<BR>\n" );
document.write( "3*a + 2*a + 1/2*a + 115 = 720<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "5.5 * a + 115 = 720<BR>\n" );
document.write( "subtract 115 from both sides to get:<BR>\n" );
document.write( "5.5 * a = 720 - 115 = 605<BR>\n" );
document.write( "divide both sides by 5.5 to get:<BR>\n" );
document.write( "a = 720/5.5 = 110<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "angle 1, 2, and 3 are each 110 degrees.<BR>\n" );
document.write( "angle 4 = 55 degrees<BR>\n" );
document.write( "angle 5 = 220 degrees<BR>\n" );
document.write( "angle 6 = 115 degrees<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the question is:<BR>\n" );
document.write( "What is the measure of the smallest angle?<BR>\n" );
document.write( "the answer is:<BR>\n" );
document.write( "55 degrees.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );