Final answer:
In the provided sentence, 'imagery' is the literary device used, as it appeals to the senses and creates a visual representation of the 'nebulous directions', making this the correct option is A.
Step-by-step explanation:
The literary device used in the sentence "The frantic woman screamed at the nebulous directions of how to pay her phone bill." is imagery. This device involves the use of descriptive language that appeals to the senses and paints a mental picture for the reader.
In this case, the phrase 'nebulous directions' creates a visual of unclear, misty, or vague guidance, allowing the reader to empathize with the woman's frustration over the complicated instructions.
It does not fit the definition of the other listed devices like simile, metaphor, or personification, and neither is it an example of repetition or a specific syntactic structure.