Based on what's in the stimulus, we know that Angie has two classes remaining to complete her degree, and it's going to take three terms (including this one) until she's done (assuming she does not fail). We need an answer choice that reflects the reality of the situation, but we don't want something that assumes too much. This is all we really know.
(D) says, "Anyone who earns a degree in psychology from the university Angela attends will have completed the course in experimental design."
This is a tricky answer choice, but it's incorrect because it's a part to whole flaw. Angela needs it to earn her degree, but that does not mean that everyone does. Maybe these two courses are electives, or maybe she has a certain subspecialty within her major of psychology. For these reasons, (D) is not something that must be true, so we can get rid of it.
(E) says, "Once Angela completes the developmental psychology course, she will have earned a degree in psychology."
(E) is something that must be true. We know that all Angela needs is these two classes to graduate, and the latter class (that must be completed after experimental design) is developmental psychology, so (E) is the correct answer choice.
Does this make sense? Let us know if you have any other questions!