Final answer:
The angles of the triangle can be found by setting up and solving an equation. After finding the value of x, substitute it back into the given expressions to find the individual angles.
Step-by-step explanation:
The angles of a triangle can be found by setting up the equation: (2x - 6) + (3x) + (3x + 18) = 180. This equation represents the fact that the sum of the angles of a triangle is always 180 degrees. Now, solve for x by combining like terms: 8x + 12 = 180. Subtract 12 from both sides: 8x = 168. Divide both sides by 8: x = 21. Now, substitute the value of x back into the given expressions to find the angles: Angle 1 = 2(21) - 6 = 36 degrees; Angle 2 = 3(21) = 63 degrees; Angle 3 = 3(21) + 18 = 81 degrees.