Question

One angle of a triangle is 2 more than four times as large as the other angle. The third angle is three times the first angle decreased by 6. What is the measure of each angle?

x+4x+2+3x-6=180

7x=180+6-2

7x=184

x=26.3

angle 1: 23.3, Angle 2: 107.1, and angle 3: 71.9

Are the angles correct?

Answer 1

You should define your variables, hard to check without knowing what x stands for

e.g.
let the "other " angle be x
then "one" angle is 4x+2
"The third angle is three times the first angle decreased by 6" ---> poor wording.
How do we know which is the "first" angle ?
the third angle could be either 3x - 6
or
3(4x+2) - 6 = 12x

case 1:
x + 4x+2 + 3x-6 = 180
8x = 184
x = 23
the angles are 23° , 94, and 63°

case 2:
x + 4x+2 + 12x = 180
17x = 180
x = 180/17
etc.

probably my first interpretation

your error is the 7x, should have been 8x