Megan was told by her dietician that she was becoming ____________ thin and should eat more.

The correct answer, "dangerously," is an adverb that appropriately modifies the adjective "thin," indicating that the level of thinness is not just concerning, but reaches a level of risk or threat to health. When combined, the phrase "dangerously thin" effectively communicates that Megan's weight loss could pose serious health risks, which aligns with the dietician's advice for her to eat more.

In contrast, the other options do not fit the grammatical structure or intended meaning. "Danger" is a noun and wouldn’t work here as it lacks the necessary form to describe the state of being thin. "Dangerous" is an adjective that could theoretically describe conditions but does not appropriately modify "thin" in this context. "Endangered," typically used to describe species at risk of extinction, does not apply to the situation and thereby fails to convey the correct sense of urgency about Megan's health.