The sentence states: "No matter how justified the usually mild and considerate Ms. Branson was in her comments, given the predicament she found herself in due to the committee's incompetence, her $\qquad$ remarks were out of character."
- "usually mild and considerate Ms. Branson": This tells us her typical demeanor is calm and kind.
- "predicament she found herself in due to the committee's incompetence": This explains why she was upset and justified in her anger.
- "her $\qquad$ remarks were out of character": This is the crucial part. It means her comments were not like her usual mild and considerate self. Therefore, the blank needs words that describe remarks that are harsh, bitter, or filled with anger/malice.

Let's look at the options:
- A. bemused: Puzzled, confused, or mildly amused. This is the opposite of angry or harsh.
- B. discerning: Having or showing good judgment. This is a positive quality, not indicative of "out of character" angry remarks.
- C. portentous: Ominous or warning of something important or disastrous. While it can imply seriousness, it doesn't convey anger or bitterness in the context of remarks being "out of character" for someone usually mild.
- D. vitriolic: Filled with bitter criticism or malice. This perfectly describes harsh, angry, and cutting remarks, fitting the "out of character" behavior for a mild person.
- E. discriminating: Recognizing or perceiving differences; discerning. Similar to "discerning," this is a positive trait related to judgment, not harshness or anger.
- F. rancorous: Characterized by bitterness or resentment. This also perfectly describes remarks filled with deep-seated ill will or animosity, fitting the "out of character" behavior for someone usually mild.

Conclusion:

Both "vitriolic" and "rancorous" describe harsh, bitter, or resentful remarks that would be "out of character" for someone usually "mild and considerate."

The correct answers are D. vitriolic and F. rancorous.