Answer:
![x=30\\y=68\\z=82](https://tex.z-dn.net/?f=x%3D30%5C%5Cy%3D68%5C%5Cz%3D82)
Step-by-step explanation:
x = measure of the first angle
y = measure of the second angle
z = measure of the third angle
The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)
![y+z=5x](https://tex.z-dn.net/?f=y%2Bz%3D5x)
The third angle is 14 more than the second
![z=y+14](https://tex.z-dn.net/?f=z%3Dy%2B14)
And remember that the sum of these three angles must be equal to 180.
![x+y+z=180](https://tex.z-dn.net/?f=x%2By%2Bz%3D180)
Let's take these equations
![y+z=5x\\z=y+14\\x+y+z=180](https://tex.z-dn.net/?f=y%2Bz%3D5x%5C%5Cz%3Dy%2B14%5C%5Cx%2By%2Bz%3D180)
If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....
![x+y+z=180\\x+(y+z)=180\\x+(5x)=180](https://tex.z-dn.net/?f=x%2By%2Bz%3D180%5C%5Cx%2B%28y%2Bz%29%3D180%5C%5Cx%2B%285x%29%3D180)
Distribute the + sign
![x+5x=180](https://tex.z-dn.net/?f=x%2B5x%3D180)
Combine like terms;
![6x=180](https://tex.z-dn.net/?f=6x%3D180)
Divide by 6.
![x=\frac{180}{6}\\ x=30](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B180%7D%7B6%7D%5C%5C%20x%3D30)
We have now defined that the measure of the first angle is 30º.
Let's take another equation... for example ![z=y+14](https://tex.z-dn.net/?f=z%3Dy%2B14)
I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.
![x+y+z=180\\30+y+(y+14)=180](https://tex.z-dn.net/?f=x%2By%2Bz%3D180%5C%5C30%2By%2B%28y%2B14%29%3D180)
Distribute the + sign and Combine like terms;
![30+y+y+14=180\\44+2y=180\\](https://tex.z-dn.net/?f=30%2By%2By%2B14%3D180%5C%5C44%2B2y%3D180%5C%5C)
Subtract 44 to isolate 2y.
![2y=180-44\\2y=136](https://tex.z-dn.net/?f=2y%3D180-44%5C%5C2y%3D136)
Now divide by 2.
![y=\frac{136}{2}\\ y=68](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B136%7D%7B2%7D%5C%5C%20y%3D68)
We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.
![x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82](https://tex.z-dn.net/?f=x%2By%2Bz%3D180%5C%5C30%2B68%2Bz%3D180%5C%5C98%2Bz%3D180%5C%5Cz%3D180-98%5C%5Cz%3D82)