Since angles \( m∠1 \) and \( m∠3 \) are vertical angles, they are congruent. This means that their measures are equal:
\[ m∠1 = m∠3 \]
Given:
\[ m∠1 = (2x + 26)^\circ \] \[ m∠3 = 14^\circ \]
Setting their measures equal to each other, we have:
\[ 2x + 26 = 14 \]
To find \( x \), first subtract 26 from both sides:
\[ 2x = 14 - 26 \] \[ 2x = -12 \]
Next, divide both sides by 2:
\[ x = -6 \]
Thus, the value of \( x \) is:
\[ \boxed{-6} \]
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