Question 8133: 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.
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! 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°.
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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.
!!!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.
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.
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.
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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:
4M - 5 + M = 180° <------- start here
5M - 5 = 180° <---- combine like terms by addition
5M = 185° <--- add 5 to both sides
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°.
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