I've attached a diagram of what I think you've described.
If I am correct, these are vertical angles, which are congruent by definition. This means you can set the angles' expressions equal to each other to solve for x.
2x + 2 = 3x - 52
2x = 3x - 54
-x = -54
x = 54
You should always check your work. To check, plug 54 for x into the equation.
2x + 2 = 3x - 52
2(54) + 2 = 3(54) - 52
108 + 2 = 162 - 52
110 = 110
Answer:
x = 54
