Answer:
{36, 66, 78}
Step-by-step explanation:
Let the measures of the three angles be f, s and t, for first, second and third. Then s + t = 4f, t = 12 + s, and f + s + t = 180.
Subbing 12 + s for t in the first equation, we get s + 12 + s = 4f.
Subbing the same in the third equation, we get f + s + 12 + s = 180
This results in two equations in two unknowns (f and s):
2s - 4f = -12
2s + f = 168.
Let's eliminate s by subtracting the first of these two equations from the second. Doing so yields 5f = 180. Then the first angle, f, or x, is 36.
Then, from 2s + f = 168, we get 2s + 36 = 168, or 2s = 132. Thus, the second angle is s = y = 66.
The sum of the three angles must be 180. Thus, 36 + 66 + t = 180, or
102 + t = 180, or t = z = 78.
The three angles are
{36, 66, 78}.
