Answer:
[tex]x=30\\y=68\\z=82[/tex]
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)
[tex]y+z=5x[/tex]
The third angle is 14 more than the second
[tex]z=y+14[/tex]
And remember that the sum of these three angles must be equal to 180.
[tex]x+y+z=180[/tex]
Let's take these equations
[tex]y+z=5x\\z=y+14\\x+y+z=180[/tex]
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....
[tex]x+y+z=180\\x+(y+z)=180\\x+(5x)=180[/tex]
Distribute the + sign
[tex]x+5x=180[/tex]
Combine like terms;
[tex]6x=180[/tex]
Divide by 6.
[tex]x=\frac{180}{6}\\ x=30[/tex]
We have now defined that the measure of the first angle is 30º.
Let's take another equation... for example [tex]z=y+14[/tex]
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.
[tex]x+y+z=180\\30+y+(y+14)=180[/tex]
Distribute the + sign and Combine like terms;
[tex]30+y+y+14=180\\44+2y=180\\[/tex]
Subtract 44 to isolate 2y.
[tex]2y=180-44\\2y=136[/tex]
Now divide by 2.
[tex]y=\frac{136}{2}\\ y=68[/tex]
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.
[tex]x+y+z=180\\30+68+z=180\\98+z=180\\z=180-98\\z=82[/tex]
