To solve for \( x \) in the given problem with vertical angles, we start by setting the measures of the angles equal to each other because vertical angles are congruent.
Given:
- \( m∠2 = 135° \)
- \( m∠4 = (4x + 15)° \)
Since the angles are vertical angles, we have: \[ 135° = 4x + 15° \]
Next, we can solve for \( x \). First, we isolate \( 4x \) by subtracting \( 15° \) from both sides: \[ 135° - 15° = 4x \] \[ 120° = 4x \]
Now, divide both sides by 4 to get \( x \): \[ x = \frac{120°}{4} = 30 \]
Thus, the value of \( x \) is \( \boxed{30} \).