document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=443605>Question 443605</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that the sum of the measures of the complements of complementary angles is 90 degrees. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305913 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305913\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let A and B be two complementary angles. We need to show that the complements of these two angles have a sum of 90. Since A and B are complementary. Then A + B = 90. Let C be the complement of A. Then A + C = 90. Let D be the complement of B. Then B + D = 90. So show that C + D = 90.<BR>\n" );
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document.write( "A + C = 90  and  B + D =90\r<BR>\n" );
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document.write( "So   A = 90 - C  and B = 90 - D<BR>\n" );
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document.write( "Since A + B = 90<BR>\n" );
document.write( "Then 90 - C + 90 - D  = 90\r<BR>\n" );
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document.write( "180 - C - D = 90<BR>\n" );
document.write( "90 = C + D<BR>\n" );
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document.write( "Which is what we wanted to show.<BR>\n" );
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document.write( "Then C (the complement of A) and D(the complement of B) are complements of each other. </SPAN>\n" );
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