Given lines $\displaystyle AB$ and $\displaystyle DC$ and the following two angles that look seemingly like same-side interior angles. The measure of angle $\displaystyle ABC$ is $\displaystyle (x+40)$ degrees and the measure of angle $\displaystyle BCD$ is $\displaystyle (2x+20)$ degrees. What are all the the values of $\displaystyle x$ such that the measures of angle $\displaystyle ABC$ and angle $\displaystyle BCD$ must be between $\displaystyle 0$ and $\displaystyle 180$ degrees and line $\displaystyle AB$ is NOT parallel to line $\displaystyle CD$?

I'm having trouble concluding the solution which is $\displaystyle -10<x<40$ or $\displaystyle 40<x<80$.