Setting Up an Advanced Mathematics Equation

[Medgirl314]

Homework Statement

Twice the supplement of angle 0 is 104 degrees greater than four times the complement of angle 0. Find 0.

Homework Equations

The Attempt at a Solution

I'm not sure where to begin. I'm good with angle relationships, all I need is the equation.

 

[Andrew Mason]

Homework Statement

Twice the supplement of angle 0 is 104 degrees greater than four times the complement of angle 0. Find 0.

Homework Equations

The Attempt at a Solution

I'm not sure where to begin. I'm good with angle relationships, all I need is the equation.

You could begin by writing an equation for the supplement and the complement of an angle θ. Then substitute in the equation that you are given:

2s = 4c + 104

AM

 

[Medgirl314]

Thank you!

 

[Medgirl314]

So the next step would be to divide both sides by 4, yielding 2s=c+26 . Then I could divide both sides by 2, yielding s=c+13. After that,I'm not sure how to proceed, because I still don't know c.

 

[Andrew Mason]

So the next step would be to divide both sides by 4, yielding 2s=c+26 . Then I could divide both sides by 2, yielding s=c+13. After that,I'm not sure how to proceed, because I still don't know c.

Use the definition of supplementary and complementary angles. But check your algebra first! You have to do the same operation to BOTH sides of the equation.

AM

 

[Medgirl314]

I could divide all the things by 2, yielding s=2c+52, but then I don't know what to do with the 2c.

 

[Andrew Mason]

I could divide all the things by 2, yielding s=2c+52, but then I don't know what to do with the 2c.

What is the definition of supplementary angle in terms of θ? What is the definition of complementary angle in terms of θ?

AM

 

[Medgirl314]

I could divide 52 by 2c, but then all I have is s=26c.

 

[Medgirl314]

Oh! Sorry! I was too busy working on randomly dividing that I forgot to check for new replies.

 

[Andrew Mason]

I could divide 52 by 2c, but then all I have is s=26c.

You have to follow the rules of algebra first. You must do the same operation to both sides of the equation.

Use s = 2c + 52

s = ? (an expression involving θ)
c = ? "

That gives you a single equation with one unknown: θ, so you have the solution.

AM

 

[Medgirl314]

Okay, I know that complementary angles add up to 90 degrees, and supplementary angles add up to 180 degrees, but I'm not sure how to work that into the equation. 2s=180=4c+104 doesn't seem to make sense.

 

[Medgirl314]

Annnnd again. xD. I need to refresh the page more often.

 

[Medgirl314]

Okay, so I have s=c+52 But I'm not quite sure what to do with my information about complementary and supplementary angles. 180-s=90-c+52 *seems* right, but that introduces more numbers and symbols that don't seem to want to go anywhere.

 

[voko]

So you have some angle $\theta$. If $s$ is its supplementary, what is it? Write this as a formula $s = ...$, where $...$ has $\theta$ in some (correct!) way.

 

[Medgirl314]

Would something along the lines of 0=(180-s=90-c+52) work out somehow? It doesn't seem right. Sorry for the trouble, I'm used to applying equations, not writing them.

 

[Medgirl314]

Or 0+s=90-c+52 ?

 

[voko]

You said: "supplementary angles add up to 180 degrees". If the supplementary angles are denoted by $\theta$ and $s$, write "supplementary angles add up to 180 degrees" as an equation involving $\theta, \ s$ and 180 degrees.

 

[Medgirl314]

Okay, so I have s=c+52 But I'm not quite sure what to do with my information about complementary and supplementary angles. 180-s=90-c+52 *seems* right, but that introduces more numbers and symbols that don't seem to want to go anywhere.

Thank you! So write that equation, abandoning this one?

 

[voko]

You do not need to abandon your previous work just yet. What you need, to continue, is to obtain equations that relate $\theta$ with $s$, and $\theta$ with $c$. Then you come back to your previous work.

The equations I am talking about follow directly from the definitions of supplementary and complimentary angles, which you know. You just need to write those definitions down algebraically.

 

[Medgirl314]

Or incorporate it into the old? Possibly s+0=180=c+52 ?

 

[Medgirl314]

Oops, we posted at the same time. Is something like the above equation correct?

 

[Andrew Mason]

Oops, we posted at the same time. Is something like the above equation correct?

Check the definition of complementary angles.

I suggest you take a step back and go through all of our suggestions and study the problem again. Be very careful with your algebra. You should be able to solve this problem now. You need to figure it out for yourself now.

AM

 

[voko]

Or incorporate it into the old? Possibly s+0=180=c+52 ?

Do not incorporate anything into anything just yet. Work out your basic equations first. You have not done so, at least here, despite our requests.

 

[Medgirl314]

s+0=180=c+52=90

Thanks, AM. Is that what you meant?

 

[Medgirl314]

Okay. Sorry, it is somewhat confusing working with two people at the same time. I'm not sure I understand the requests as you meant them. Voko, when AM left off right before you came in, we had s=c+52
Would you mind restating the next step?

 

[voko]

Okay. Sorry, it is somewhat confusing working with two people at the same time. I'm not sure I understand the requests as you meant them. Voko, when AM left off right before you came in, we had s=c+52

And I think AM told you it was not correct.

Would you mind restating the next step?

AM told you, as did I, that you need to convert your definitions of complimentary and supplementary angles into an algebraic form. That will give you two equations. Together with the one you got previously (provided it is corrected), that will give you a complete system of equations required to solve this problem.

 

[Medgirl314]

Okay. So what we are looking for is to leave his *original* equation the same, but come up with two new equations, which are simply the angle definitions in algebraic form?

 

[voko]

Correct.

 

[Medgirl314]

Good.Now we're getting somewhere. I thought you meant to combine those equations with the previous equation.
<0=90-c
<0=180-s

Sorry for the weird signs, they are meant to indicate angles.

 

[voko]

I suggest that you use letter A for what you denoted as <0. So A means "the angle", and c and s are the angles complimentary and supplementary to it, respectively.

Can you recast these equations as c = ... and s = ...? Once you are done with that, you can substitute those into the original equation.

 

[Medgirl314]

C=90-A
S=180-A

Like that?

 

[voko]

Continue :)

 

[Medgirl314]

That would make my three equations the following:
2s=4c+104 degrees=0
S=180-A
C=90-A

 

[Medgirl314]

Haha, I tried to click thanks again, and it said I gave out to much Reputation in the last 24 hours. XD

 

[Medgirl314]

So now I need to work the equations together. Am I adding like terms, or substituting the appropriate equations where I left s and c?

 

[voko]

Do whatever works best for you. Your objective is to obtain A and get rid of c and s.

 

[Medgirl314]

Okay, after plugging in my new equations, I get 2(180-A)=(90-A)+104 degrees=A

 

[Medgirl314]

If I apply the distributive property in the first part, I get (360-A)=(90-A)+104=A

 

[Medgirl314]

Can I add 104 to 90, or does that violate an algebraic rule I am forgetting?

 

[voko]

Okay, after plugging in my new equations, I get 2(180-A)=(90-A)+104 degrees=A

The right hand side had 4c originally.

 

[Medgirl314]

Right, thanks. So: 2(180-A)=4(90-A)+104 degrees=A ?

 

[voko]

Why do you have two equality signs there? Where does the second one come from?

 

[Medgirl314]

I was attempting to state that those two equations are equal to both each other and A. Is the =A not supposed to be there?

 

[voko]

The original equation was 2s = 4c + 104. You substituted s = 180 - A and c = 90 - A into it. How would that bring about = A to it?

 

[Medgirl314]

No idea. It snuck it's way in there. So: 2(189-A)=4(90-A)+104 degrees.

 

[Medgirl314]

Shall I apply the distributive property?

 

[voko]

I hope 189 was a typo.

Your goal to is to transform the equation to A = ..., where the right hand side does not have A. Use whatever algebraic rules that help you achieve that. It is not too hard.

 

[Medgirl314]

Major typo. It was meant to be 180. The nine is, of course, right next to the zero, and I was typing too quickly.

 

[Medgirl314]

Applying distributive property: (360-A)=(360-A)+104.
Combining like terms: (720-2A)+104

Why doesn't that seem right?

 

[Medgirl314]

Probably because I eliminated the equal sign...