Since angles \( m\angle 1 \) and \( m\angle 3 \) are vertical angles, they are equal in measure. This gives us the equation:
\[ m\angle 1 = m\angle 3 \]
Substituting the given expressions into the equation:
\[ 2x + 26 = 14 \]
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:
\[ \boxed{-6} \]
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