document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165224>Question 165224</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0764122967/algebrahomeworkh>Lets Review Math A</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> QUESTION: In isosceles triangle ABC the ratio of the measure of vertex angle A to the measure of angle B is 2 to 5. Find angle C.\r<BR>\n" );
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document.write( "<br>1st APPROACH: we know that in an isosceles triangle two angles are the same and the sides opposite them are also the same.\r<BR>\n" );
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document.write( "<br>Since this problem doesn't tell you which is the base vertex in this isosceles triangle, I have assumed it to be 5x. Because of \"RULE:\" <br>the length of each side is less than the sum of the lengths of the other two sides and greater than the difference between these lengths....3less than x less than 7. Therefore x is in the range of 4, 5, 6. <BR>\n" );
document.write( "<br>2x+5x+5x=180<BR>\n" );
document.write( "<br>12x=180<BR>\n" );
document.write( "<br>x=15\r<BR>\n" );
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document.write( "Angle C is 75 degrees<BR>\n" );
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document.write( "2nd APPROACH: we know that in an isosceles triangle two angles are the same and the sides opposite them are also the same. <BR>\n" );
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document.write( "Since we already used 5x as the base vertex in our previous approach lets assume 2x is the base angle, this time, because it's an isosceles triangle. <BR>\n" );
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document.write( "2x+2x+5x=180<BR>\n" );
document.write( "<br>9x=180<BR>\n" );
document.write( "<br>x=20\r<BR>\n" );
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document.write( "Angle C is 40 degrees<BR>\n" );
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document.write( "BOOKS ANSWER IS 100 degrees, why? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121825 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=121825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's a quick note about what the ratio is really saying:\r<BR>\n" );
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document.write( "Since the ratio is vertex angle A to the measure of angle B, this means that we have this ratio:\r<BR>\n" );
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document.write( "A:B ---> 2:5\r<BR>\n" );
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document.write( "So this means that the vertex angle is SMALLER than the base angle. However, if you have a base angle of 40 degrees, this means that the vertex angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180-2%2A40=180-80=100 ALIGN=MIDDLE  ALT=\"180-2%2A40=180-80=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the vertex angle is larger (not smaller) than the base angle. So this effectively rules out the \"2nd Approach\" answer. Remember, the ratio is vertex:base angle (not the other way around)\r<BR>\n" );
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document.write( "However, I agree with your first approach. That answer is correct. You'll find that the base angles are 75 degrees and the vertex angle is 30 degrees. Since the ratio of 30:75 reduces to 2:5, this verifies the answer.\r<BR>\n" );
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document.write( "Note: it is IMPOSSIBLE to have both an isosceles triangle AND have a base angle that is greater than 90 degrees. Why? Base angles are equal. So if there is an obtuse base angle, there are really 2 obtuse angles in the triangle (which is impossible; triangles can only have at most one obtuse angles). So this means that either the book is wrong or maybe you read the wrong answer. </SPAN>\n" );
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