Question

____ is the degree to which someone is not angry, depressed, anxious, emotional, insecure, or excitable.

Answer 1

C. emotional stability.

A. Agreeableness is what it sounds like... Willing to be agreeable... Willing to agree.
B. Conscientiousness is also what it sounds like...to be conscious of what's going on around you and within you (external and internal locus of control).
D. Disposition is how you view things...how you "valence" something (valence means to label something as positive or negative); your response in context to disposition is usually stable and predictable over time.
E. Extraversion basically just refers to how social or outgoing you are.

Even though emotional stability is the correct answer, it's important to understand emotional stability (aka emotional regulation) is on a scale. We all feel angry, anxious, depressed, emotional, insecure, and excitable multiple times in our lives. These are normal human emotions! However, in psychology, we start to call it "abnormal", or say there's a "lack of emotional regulation/stability" when these types of negatively valenced emotions are pervasive in everyday life. This is why the question specifies "the DEGREE to which".

Hope this helps!