document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=926825>Question 926825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The measures of two complementary angles are in the ratio 2:3. What is the measure of the smaller angles? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562503 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=562503\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> angles are complementary so their sum is 90.<BR>\n" );
document.write( "a equals one of the angles<BR>\n" );
document.write( "b = the other angle.<BR>\n" );
document.write( "the angles are in a ratio of 2/3.<BR>\n" );
document.write( "a/b = 2/3<BR>\n" );
document.write( "multiply both sides of the equation by b to get:<BR>\n" );
document.write( "a = 2b/3<BR>\n" );
document.write( "you have a + b = 90 because the angles are complementary.<BR>\n" );
document.write( "you know that a = 2b/3<BR>\n" );
document.write( "replace a with 2b/3 in the equation of a + b = 90 to get:<BR>\n" );
document.write( "2b/3 + b = 90<BR>\n" );
document.write( "since b is equivalent to 3b/3, the equation becomes:<BR>\n" );
document.write( "2b/3 + 3b/3 = 90<BR>\n" );
document.write( "combine fractions with the same denominator together to get:<BR>\n" );
document.write( "5b/3 = 90<BR>\n" );
document.write( "multiply both sides of the equation by 3 to get:<BR>\n" );
document.write( "5b = 270<BR>\n" );
document.write( "divide both sides of the equation by 5 to get:<BR>\n" );
document.write( "b = 54 degrees.<BR>\n" );
document.write( "since a = 2b/3, then a must be equal to 2*54/3 = 36 degrees.<BR>\n" );
document.write( "a = 36 degrees<BR>\n" );
document.write( "b = 54 degrees<BR>\n" );
document.write( "a+b = 90 so the answer looks good.<BR>\n" );
document.write( "the smaller angle measures 36 degrees.\r<BR>\n" );
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document.write( "another way to look at it.<BR>\n" );
document.write( "angles are in a ratio of 2 to 3.<BR>\n" );
document.write( "the sum of the angles will be x times each of them.<BR>\n" );
document.write( "you get 2x + 3x = 90 <BR>\n" );
document.write( "this is because the angles are complementary and their sum is therefore equal to 90.<BR>\n" );
document.write( "combine like terms to get 5x = 90<BR>\n" );
document.write( "divide both sides of this equation by 5 to get x = 18.<BR>\n" );
document.write( "the smaller angle is 2x = 2 times 18 = 36 degrees.<BR>\n" );
document.write( "the larger angle is 3x = 3x = 3 * 18 = 54 degrees.\r<BR>\n" );
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