Where is my mistake? - Equations?

Question

X=number of degrees of the smallest angle
Y=number of degrees of the second angle
Z=number of degrees of the largest angle

X+Y+Z=180
Z=4X
Y=Z-X

Z=180-X-Y
Z=180-4Z-Y
Z=180-4Z-X-Z
Z=180-5Z-X
Z=180-5Z-4Z
Z=180-9Z
10Z=180
Z=180/10
Z=18

X=4*18
X=64

Y=64-18
Y=46

X=64
Y=46
Z=18

64+46+18= 128. I'm SUPPOSED to get 180. Where is my mistake?

For reference, here is the actual question:
The sum of the three angles in the triangle is 180 degrees. Find the measures of the angles if the angles of the largest is four times as large as the smallest and equal to the sum of the two smaller.

Whoops! A typo! It was supposed to be X=4Z.
NoT Z=4X

Answer 1

Your mistake is that X does not equal 4Z. X equals 1/4Z. Follow me:

Z=180-X-Y
Z=180-1/4Z-(Z-X)
Z=180-1/4Z-(Z-1/4Z)
Z=180-1/4Z-3/4Z
Z=180-Z
2Z=180
Z=90

Z=4X
90=4X
90/4=X
X=22.5

Y=Z-X
Y=90-22.5
Y=67.5

X+Y+Z=180
22.5+67.5+90=180

Answer 2

Here is how to start:

Y=4x-x Substituing Z from Z=4x Therefore
Y=3x Then
X+3X+4x=180 substituting the above Y=3x
8x=180
x=22.5
Now that you know the value of X substitute it back into Y=3x and Z=4X and this means,
Z=90
Y=67.5

22.5+67.5+90=180

Answer 3

Smallest angle is X. big angle is 4X. The thirt angle is Y.
so, 180=4x+x+y
and 4x=x+y
therefore 180=4x+4x
which gives x=180/8=22.5
so y=4x-x=3x=22.5*3=67.5
and the big angle=x+y=90

easy haaa.....

Answer 4

You replaced X with 4Z. That's not correct.

Z = 4X
X = Z/4

I'd recommend solving for X first, instead of Z.

Answer 5

z=90 so you made a mistake from the beginning. You can probably solve it from there.