If a transversal intersects two lines such that the bisectors of pair of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

In the figure, $\mathrm{A}\mathrm{B}\mathrm{}\left|\right|\mathrm{}\mathrm{C}\mathrm{D}\mathrm{}$ and $\mathrm{}\mathrm{C}\mathrm{D}\mathrm{}\left|\right|\mathrm{}\mathrm{E}\mathrm{F}$. Also $\mathrm{E}\mathrm{A}\perp \mathrm{A}\mathrm{B}.$ If $\mathrm{\angle }\mathrm{B}\mathrm{E}\mathrm{F}=55°$, find the values of $\mathrm{x}.\mathrm{}\mathrm{y}\mathrm{}$ and $\mathrm{}\mathrm{z}.$

In the given figure, $\mathrm{A}\mathrm{B}\mathrm{}\left|\right|\mathrm{}\mathrm{C}\mathrm{D}\mathrm{}\left|\right|\mathrm{}\mathrm{E}\mathrm{F}$. Find the value of $\mathrm{x}$.

For what value of $\mathrm{x}$ will the lines $\mathrm{l}$ and $\mathrm{m}$ be parallel to each other.

In the figure, l $\mathrm{}\left|\right|\mathrm{}\mathrm{m}$ and t is a transversal. If $\mathrm{\angle }1:\mathrm{\angle }2=3:7,$ then find the degree measures of all angles.