document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=764136>Question 764136</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If two angels of a triangle are acute angles,then the third angle is?\r<BR>\n" );
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document.write( "Less then the sum of the other two angles\r<BR>\n" );
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document.write( "Is an acute angle\r<BR>\n" );
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document.write( "Is an obtuse angle\r<BR>\n" );
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document.write( "Is the largest angle 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 #465222 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=465222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "All of the choices are possible, but none of them is certain.\r<BR>\n" );
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document.write( "Proof:  Let angle A and angle B be the given acute angles and angle C be the third angle.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 0\ <\ m<A\ <\ 90\">\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 \ \ \ \ \ \ \ \ \ \ 0\ <\ m<B\ <\ 90\">\r<BR>\n" );
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document.write( "By definition of acute\r<BR>\n" );
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document.write( "Since we can choose any value in that range for angles A and B, let's choose 89 degrees for each one.\r<BR>\n" );
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document.write( "Then the sum of the measures of the two angles is then 178 degrees.  Since the sum of the three angles of any triangle is 180, Angle C must measure 2 degrees, which makes Angle C an acute angle.\r<BR>\n" );
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document.write( "So far we have validated the first two answers and invalidated the last two.\r<BR>\n" );
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document.write( "Now, let the measures of angle A and angle B each be 1 degree, making the measure of angle C 178 degrees.\r<BR>\n" );
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document.write( "This situation invalidates the first two answers but validates the last two.\r<BR>\n" );
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document.write( "Therefore the fact that two of the angles of a triangle are acute tells you nothing substantive except that you actually have a triangle.   In fact EVERY triangle has at least two acute angles.  I'll leave the proof of that assertion as an exercise for the student.\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( " </SPAN>\n" );
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