document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=276147>Question 276147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three angles of a pentagon are 130', 90', and 80'. Of the remaining two angles, one is 30' more than twice the other. What is the sum of the smallest two angles? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201300 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=201300\">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'm going to just assume that you used ' to mean degrees of arc as opposed to minutes of arc which is the traditional meaning of that symbol.\r<BR>\n" );
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document.write( "The sum of the interior angles of any <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\">-gon is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(n\ -\ 2\right)180\">\r<BR>\n" );
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document.write( "For a pentagon, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> is 5.  So calculate the sum of the interior angles of a pentagon.\r<BR>\n" );
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document.write( "From that calculation result, subtract the sum of 130°, 90°, and 80° leaving you the sum of the measures of the remaining two angles.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the measure of the smaller angle.  Then the larger angle must measure <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x\ +\ 30\">.  Furthermore, the sum:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 2x\ +\ 30\">\r<BR>\n" );
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document.write( "must be equal to the result of the previous calculation.  Putting it all together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 2x\ +\ 30\ =\ \left(5\ -\ 2\right)180\ -\ \left(130\ +\ 90\ +\ 80\right)\">\r<BR>\n" );
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document.write( "Just solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> to get the measure of the smaller of the two remaining angles.  This will turn out to be the smallest of all 5 angles.  The other one will be the largest of all 5.  Discover its measure by multiplying the measure of the smallest angle by 2 and adding 30 degrees.  Now that you know the measure of all 5 angles, it should be an easy matter to add the measures of the two smallest ones.\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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