Answer:
Not quite in proof format but here's a short explaination. You should be able to fill out the table yourself.
It is given that <T=<Y and <V+<U=180 degrees
<T=<Y are corresponding angles. Corresponding angles are congruent when the two lines (that the third line crosses to make a transversal) are parallel. So, l1 and l2 are parallel.
<V+<U are supplementary angles. They are same side interior angles. Same side interior angles are supplementary when two lines of the transversal are parallel (basically same thing as above, just different type of angle). So, l3 and l4 are parallel.
<R=<U because they are alternate interior angles. Alternate interior angles are congruent when the two lines are parallel (you have proved that l3 and l4 are parallel above).
<P=<C because they are alternate exterior angles. Alternate exterior angles are congruent when the two lines are parellel (you have proved that l1 and l2 are parallel above).
