document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142324>Question 1142324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What angle is a fifth of its complement </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763036 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x be the angle.\r<BR>\n" );
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document.write( "let y be its complement.\r<BR>\n" );
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document.write( "x + y = 90 if the angles are complements of each other.\r<BR>\n" );
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document.write( "if the angle is 1/5 of its complement, then y = 5x.\r<BR>\n" );
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document.write( "replace y with 5x in the equation of x + y = 90 to get:\r<BR>\n" );
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document.write( "x + 5x = 90\r<BR>\n" );
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document.write( "combine like terms to get 6x = 90\r<BR>\n" );
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document.write( "solve for x to get x = 90/6 = 15 degrees.\r<BR>\n" );
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document.write( "the angle is 15 degrees.\r<BR>\n" );
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document.write( "its complement is 5 times as large, making it equal to 5 * 15 = 75 degrees.\r<BR>\n" );
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document.write( "the angle plus its complement is equal to 90 degrees because 15 + 75 = 90.\r<BR>\n" );
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document.write( "your solution is that the angle is 15 degrees.\r<BR>\n" );
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document.write( "15 / 75 = 1 / 5.\r<BR>\n" );
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document.write( "another way to solve this is as follows.\r<BR>\n" );
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document.write( "the angle is x.\r<BR>\n" );
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document.write( "the complement is 90 - x.\r<BR>\n" );
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document.write( "the angle is 1/5 its complement leads to x = 1/5 * (90 - x)\r<BR>\n" );
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document.write( "simplify to get x = 1/5 * 90 - 1/5 * x\r<BR>\n" );
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document.write( "simplify to get x = 18 - 1/5 * x\r<BR>\n" );
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document.write( "add 1/5 * x to both sides of the equation to get 6/5 * x = 18\r<BR>\n" );
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document.write( "multiply both sides of this equation by 5/6 to get x = 5/6 * 18\r<BR>\n" );
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document.write( "solve for x to get x = 15.\r<BR>\n" );
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document.write( "same answer solved in a different way.\r<BR>\n" );
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