Since angles \( m∠1 \) and \( m∠3 \) are vertical angles, they are equal. Therefore, we can set up the equation:
\[ m∠1 = m∠3 \]
Substituting the given expressions, we have:
\[ 2x + 26 = 14 \]
Now, we can solve for \( x \). First, subtract 26 from both sides:
\[ 2x = 14 - 26 \]
This simplifies to:
\[ 2x = -12 \]
Next, divide both sides by 2:
\[ x = -6 \]
Thus, the value of \( x \) is:
\[ \boxed{-6} \]