Setting Up an Advanced Mathematics Equation

1. Sep 22, 2013

Medgirl314

1. The problem statement, all variables and given/known data
Twice the supplement of angle 0 is 104 degrees greater than four times the complement of angle 0. Find 0.

2. Relevant equations

3. The attempt at a solution
I'm not sure where to begin. I'm good with angle relationships, all I need is the equation.

2. Sep 22, 2013

Andrew Mason

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

3. Sep 22, 2013

Medgirl314

Thank you!

4. Sep 22, 2013

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.

5. Sep 22, 2013

Andrew Mason

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

6. Sep 22, 2013

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.

7. Sep 22, 2013

Andrew Mason

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

AM

8. Sep 22, 2013

Medgirl314

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

9. Sep 22, 2013

Medgirl314

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

10. Sep 22, 2013

Andrew Mason

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

11. Sep 22, 2013

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.

12. Sep 22, 2013

Medgirl314

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

13. Sep 22, 2013

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.

14. Sep 22, 2013

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.

15. Sep 22, 2013

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.

16. Sep 22, 2013

Medgirl314

Or 0+s=90-c+52 ?

17. Sep 22, 2013

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.

18. Sep 22, 2013

Medgirl314

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

19. Sep 22, 2013

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.

20. Sep 22, 2013

Medgirl314

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