document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117645>Question 117645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the measure of each base angle of an isosceles triangle if the vertex angle measures 76 degrees </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85853 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=85853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the angles of a triangle are 180 degrees.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If the vertex angle of the triangle is 76 degrees, that means that the two angles that remain<BR>\n" );
document.write( "must result in a total of 180 degrees when they are added to 76 degrees. Think of it this<BR>\n" );
document.write( "way in equation form: if the three angles of a triangle are A, B, and C, then<BR>\n" );
document.write( "their measures <BR>\n" );
document.write( "add to 180 degrees as follows:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "mA + mB + mC = 180<BR>\n" );
document.write( ".<BR>\n" );
document.write( "where mA represents the measure of angle A, mB the measure of angle B, and mC the measure of<BR>\n" );
document.write( "angle C.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "In this problem you are told that the measure of one of the angles (let's say mA) is 76 <BR>\n" );
document.write( "degrees. In the equation for the sum of the angles, we substitute 76 for mA to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "76 + mB + mC = 180<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We get rid of the 76 on the left side by subtracting 76 from both sides to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "mB + mC = 180 - 76 = 104<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So the equation has simplified to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "mB + mC = 104<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now think in terms of isosceles triangles. The unique things about isosceles triangles are<BR>\n" );
document.write( "that two of the sides have the same lengths, and the measures of the two base angles are <BR>\n" );
document.write( "also equal.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Therefore, regarding the two base angles we know mB = mC. So we can substitute mB for mC in <BR>\n" );
document.write( "our equation. When we make that substitution we get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "mB + mB = 104<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Adding the two terms on the right side results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2*mB = 104<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We can solve for mB by dividing both sides of this equation by 2 and we get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "mB = 104/2 = 52 degrees<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since the measure of one base angle equals 52 degrees we know that the measure of the other<BR>\n" );
document.write( "base angle also equals 52 degrees.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So in the given triangle the measures of the three angles are 52 degrees, 52 degrees, and<BR>\n" );
document.write( "76 degrees. The total of these 3 measures is 180 degrees, just as it must be. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem and how to solve it.<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );