Since angles \( m<1 \) and \( m<3 \) are vertical angles, they are congruent. Therefore, we can set their measurements equal to each other:
\[ m<1 = m<3 \]
Given that \( m<1 = 2x + 26 \) and \( m<3 = 14 \), we can write the equation:
\[ 2x + 26 = 14 \]
Now, to solve for \( x \), we first subtract 26 from both sides:
\[ 2x = 14 - 26 \] \[ 2x = -12 \]
Next, we divide both sides by 2:
\[ x = \frac{-12}{2} \] \[ x = -6 \]
Therefore, the value of \( x \) is \(-6\).