Vertical angles are always congruent, which means that they have the same measure. Therefore, we can set the measure of angle 1 equal to the measure of angle 2 and solve for x.
106 = 3x - 75
To solve for x, we can add 75 to both sides of the equation:
106 + 75 = 3x
Simplifying the left side:
181 = 3x
Finally, we can divide both sides by 3 to isolate x:
x = 60.33
Therefore, the value of x that makes the vertical angles congruent is approximately 60.33 degrees.