Correct option is A
The correct substitution of the quoted words is "an industrious".
Explanation: "A industriously" is incorrect because "industriously" is an adverb, inappropriate for describing a noun. "Industrious" is the correct adjective form, and since it starts with a vowel sound, "an" is the correct article instead of "a".
Grammatical rule used: Use "an" before words that start with a vowel sound.
Example: She is an industrious worker.