# 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.

## The Attempt at a Solution

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

Homework Helper

## Homework Statement

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

## 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

• 1 person
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.

Homework Helper
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.

Homework Helper
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.

Homework Helper
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.

• 1 person
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?

Homework Helper
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

• 1 person
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.

• 1 person
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?