Answer:
A) Stubborn
Explanation:
<em>Inflexible</em> refers to something or someone that is not able or willing to change or adapt their opinions, habits, attitude or ideas, similar to a stubborn person who refuses to change their opinions, habits, attitude, ideas or positions, especially in spite of good arguments or reasons to do so.
In the passage, the sentence "He answered with inflexible humility" conveys that he answered with a determined or stubborn humility, meaning that he had no intention to act without humility.
