document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=8133>Question 8133</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the measures of two supplementary angles, angle N and angle M, if the measures of angle N is 5 less than 4 times the measure of angle M. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4469 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=4469\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So, if those two angles are supplementary, their total should be 180°. Let's call them N and M like they did. So we know so far that N + M = 180°.\r<BR>\n" );
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document.write( "Now there's that tricky part where they tell you about the relationship between angle N and angle M. Just by reading the problem, angle N is larger than angle M. How'd that happen? Ignore the \"5 less than\" for now. The sentence would then read \"angle N is 4 times the measure of angle M\". That would make N = 4M because it would take 4M's to equal an N. \r<BR>\n" );
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document.write( "!!!WARNING: Just because angle N is bigger, many will make the mistake of saying 4N = M with the reasoning that \"if N is bigger, then it's got to get the 4 multiplied to it.\" It's the actual opposite. The angle M is smaller, so it's the one that needs some boosting (multiplying it by 4, as the problem said) to equal the larger.\r<BR>\n" );
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document.write( "Alright. Now, where does that \"5 less than\" come into play? That's another point of confusion. When you read the sentence, you'll notice that angle N isn't quite quadruple of angle M. It's actually less than quadruple of M, by what? It would be by 5. So angle N = 4M - 5. Another wrong thing that many people do is to say \"5 - 4M\" just because the sentence mentions the 5 first before the 4M.\r<BR>\n" );
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document.write( "WORD PROBLEM TIP: When you see the phrase \"is P less than Q\", it ALWAYS translates to Q - P. WHY? Say that you're 16 years old. You then tell somebody that your brother is two years younger than you. That would make him 14. So your brother's age B is your age - 2 (14 = 16 - 2) NOT \"2 minus your age\" because that obviously gives a wrong (negative age) answer.<BR>\n" );
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document.write( "So now we've got the N = 4M - 5 nailed down. And we still have the N + M = 180°. We'll do a substitution. We'll put 4M - 5 instead of the N in the N + M = 180° equation. That way, the equation would only be written in 1 variable. We now have:\r<BR>\n" );
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document.write( "4M - 5 + M = 180° <------- start here\r<BR>\n" );
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document.write( "5M - 5 = 180° <---- combine like terms by addition\r<BR>\n" );
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document.write( "5M = 185° <--- add 5 to both sides\r<BR>\n" );
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document.write( "M = 37° <----- If M (the smaller angle) is 37°, then the bigger angle, N, must be quadruple that (so that's 4*37° or 148°) but it's 5 less, so 148° - 5° = 143°. \r<BR>\n" );
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