Vertical angles are equal, so we can set the measures of the angles equal to each other to solve for \( x \).
Given:
- Measure of angle 1: \( m\angle 1 = 106 \)
- Measure of angle 2: \( m\angle 2 = 3x - 75 \)
Since these angles are vertical angles, we have:
\[ m\angle 1 = m\angle 2 \]
This leads to the equation:
\[ 106 = 3x - 75 \]
To solve for \( x \), you can rearrange this equation. None of the provided options perfectly match the standard way to write the equation, but the correct equation to start solving for \( x \) is essentially:
\[ 3x - 75 = 106 \]
Thus, the correct choice from your options is:
3x - 75 = 106