Question

The figure below shows a transversal t which intersects the parallel lines PQ and RS:

Answer 1

There are many ways to prove this, but the quickest and easiest way is to use the property of corresponding angles. If two lines are parallel with a line intersecting them both, their corresponding angles formed by the intersecting line are equal.
In this case, the corresponding angles are:
1 and 5
2 and 6
3 and 7
4 and 8
Since angle 4 and 8 are corresponding angles, they are necessarily equal.