Vertical angles are equal to each other, so to solve this, you can set the angle measures equal to each other and solve for x.
Z = Y Replace X and Y with their values
4x - 17 = 2x + 7 Isolate the value. Start by adding 17 to both sides
4x = 2x + 24 Subtract 2x from both sides
2x = 24 Divide both sides by 2
x = 12