document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237386>Question 237386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In isosceles ABC, B is the vertex. The measure of B can be represented as (8x-6). The measure of A can be represented as (3x+2). Find the measure of all three angles of the triangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174570 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "I presume that you mean B to be the angle that is different in measure from the other two angles in the isosceles triangle.  The word vertex is used incorrectly in this context.  All triangles, regardless of their configuration have three vertices.  In an isosceles triangle, two of the vertices have angles that are equal in measure.\r<BR>\n" );
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document.write( "Given a correct assumption on my part, if B is the unequal angle, then angle A must be congruent to angle C, hence their measures are equal.  Therefore if angle A measures <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3x\ +\ 2\"> then angle C must measure <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3x\ +\ 2\"> also.\r<BR>\n" );
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document.write( "We know that the sum of the measures of the interior angles of a triangle is 180 degrees or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \pi\"> radians.\r<BR>\n" );
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document.write( "So we can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (8x\ -\ 6)\ +\ (3x\ +\ 2)\ +\ (3x\ +\ 2)\ =\ 180\ \Rightarrow\ 14x\ -\ 2\ =\ 180\ \Rightarrow\ 14x\ -\ 2\ =\ 180\ \Rightarrow\ x\ =\ 13\">\r<BR>\n" );
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document.write( "From which you can calculate:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ B\ =\ 8(13)\ -\ 6\ =\ 98\"> degrees.\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ C\ =\ 3(13)\ +\ 2\ =\ 41\"> degrees.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 98\ +\ 41\ + 41\ =\ 180\">\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (8x\ -\ 6)\ +\ (3x\ +\ 2)\ +\ (3x\ +\ 2)\ =\ \pi\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 14x\ -\ 2\ =\ \pi\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\pi\ +\ 2}{14\">\r<BR>\n" );
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document.write( "From which you can calculate\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ B\ =\ \frac{4\pi\ +\ 8}{7}\ -\ 6\ =\ \frac{4\pi\ -\ 34}{7}\"> radians\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A\ =\ C\ =\ \frac{3\pi\ +\ 6}{14}\ + 2\ =\ \frac{3\pi\ +\ 34}{14}\"> radians\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{4\pi\ -\ 34}{7}\ +\ \frac{3\pi\ +\ 34}{14}\ +\ \frac{3\pi\ +\ 34}{14}\ =\ \pi\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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