Why is my equation not working for finding the angles of a triangle?

[LogarithmLuke]

So given a problem where you have a triangle. One angle in the triangle is 4 times larger than another angle. How big are each of the angles?

So i set up the equation 4x+x+180-5x=180

One angle is 4 times large than another, hence 4x. The angles must add up to 180 because it's a triangle. The last one has to be 180 minus the the two others(4x+x). I see that the equation won't work because the x's cancel out, but i don't understand why this is not correct. I feel like I am missing out on something very basic and obvious but i can't seem to figure out what it is. Could someone help me out?

Btw i wasnt sure whether to put this here or in the homework section, Perhaps you mods could move it if it doesen't belong here?

 

[RUber]

It is because you don't have enough information.
You could have (1, 4, 175), (2, 8, 170), etc.

 

[RUber]

To better explain, you have what is called an underdetermined system.
$\left\{ \begin{array}{l l } x + y + z = 180 \\ 4x - y = 0 \end{array} \right.$
Note that you have 3 variables and only two equations.
You can narrow down the possibilities, by constraining x, y, z to be positive values. Then you have 0< x < 36, giving 0 < y < 144, but still unless you know something else about the system, you will not find an answer.

In your equation that you built, you essentially used the same constraint equation twice. This gave you a tautological (always true) equation, 180 = 180.
Using x + y + z = 180 to define z = 180-x - y, and then substituting back into the same equation gives x + y + 180 - x -y = 180, just like you found. If you could find another relationship, you could hope to solve for one, and thus all, of the angles.