Step 1 :Given that $m \angle 1=111^{\circ}$, we know that when a transversal crosses parallel lines, alternate interior angles are congruent. Therefore, the measure of angle 4 should be equal to the measure of angle 1.
Step 2 :So, $m \angle 4 = \boxed{111^{\circ}}$.
Step 3 :Given that $m \angle 2=(3 x-15)^{\circ}$ and $m \angle 3=(2 x-30)^{\circ}$, we know that when a transversal crosses parallel lines, corresponding angles are congruent. Therefore, the measure of angle 2 should be equal to the measure of angle 3.
Step 4 :We can set up an equation and solve for x: $3x - 15 = 2x - 30$.
Step 5 :Solving the equation, we find that the value of $x$ is $\boxed{-15}$.