Answer:
If you want to know how to solve this trapezoid problem, you came to the right place. I will show you the steps in a funny way, because math is more fun when you laugh. Here we go:
a. AFAS and ATAS are like twins, because they have the same length. They are both half of AD, because F is the middle child of the family AD. EBES and ECES are also like twins, because they have the same length. They are both half of BC, because E is the middle child of the family BC. This is called the midpoint theorem, and it's very useful for finding twins.
b. ZSTA and ZSFA are like old friends, because they always add up to 180 degrees. They are called supplementary angles, and they happen when a line crosses two parallel lines. In this case, the line is A_F and the parallel lines are AB and CD. ZETB and ZECB are also like old friends, because they always add up to 180 degrees. They are also supplementary angles, and they happen when a line crosses two parallel lines. In this case, the line is EC and the parallel lines are AB and CD.
c. LAST and LASF are also like old friends, because they also add up to 180 degrees. They are also supplementary angles, and they happen when a line crosses two parallel lines. In this case, the line is SF and the parallel lines are AB and CD. But ST and SF are not like old friends, because they are not angles at all. They are segments, and they don't care about parallel lines or transversals. They just want to be left alone.