document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116501>Question 116501</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the measure of the third angle of a triangle in which the measures of two angles are w and (w+20). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84708 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84708\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the angles in a triangle is 180 degrees.<BR>\n" );
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document.write( "Suppose that you knew one of the angles in the triangle was 20 degrees and another angle in<BR>\n" );
document.write( "the triangle was 80 degrees. How would you find the third angle? You can do it by adding the<BR>\n" );
document.write( "two angles that you know ... 20 degrees + 80 degrees = 100 degrees. Since these two angles<BR>\n" );
document.write( "provide 100 degrees of the 180 degrees in the triangle, the third angle must provide the <BR>\n" );
document.write( "rest. Therefore, the third angle must be 180 degrees minus 100 degrees and this is 80 degrees.<BR>\n" );
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document.write( "The problem you are given can be worked in a similar manner.<BR>\n" );
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document.write( "You are given that two of the angles of a triangle are w and w + 20. If you add these two<BR>\n" );
document.write( "angles you get:<BR>\n" );
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document.write( "w + (w + 20) = w + w + 20 = 2w + 20<BR>\n" );
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document.write( "The third angle of the triangle must be the remainder after you subtract the sum of the two<BR>\n" );
document.write( "known angles from 180 degrees. So subtract 2w + 20 from 180 degrees:<BR>\n" );
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document.write( "180 - (2w + 20)<BR>\n" );
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document.write( "If you have terms inside a set of parentheses that is preceded by a minus sign, you can remove<BR>\n" );
document.write( "the parentheses if you change the signs of the terms inside the parentheses. Applying that<BR>\n" );
document.write( "rule we remove the parentheses by changing the 2w inside the parentheses to -2w and the +20<BR>\n" );
document.write( "inside the parentheses to -20. So the problem becomes:<BR>\n" );
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document.write( "180 - 2w - 20<BR>\n" );
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document.write( "Combine the 180 and the -20 to get 160 and the answer becomes that the third angle equals:<BR>\n" );
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document.write( "160 - 2w<BR>\n" );
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document.write( "Check: do the three angles: w, w + 20, and 160 - 2w add up to be 180 degrees?<BR>\n" );
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document.write( "w + w + 20 + 160 - 2w<BR>\n" );
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document.write( "The w + w -2w equals 2w - 2w and this cancels out to zero. What remains is 20 + 160 and <BR>\n" );
document.write( "this does equal 180. So the three angles correctly add to 180 degrees. The answer that<BR>\n" );
document.write( "the third angle is 160 - 2w therefore is correct.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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