This question tests your understanding of gerunds and perfect forms in English grammar, specifically after the preposition "for".

The structure is: Subject + be verb + adjective + with someone + for + [verb form]. The word "for" is a preposition, and a fundamental rule is that prepositions must be followed by a noun or a gerund (a verb form ending in -ing that functions as a noun). This immediately eliminates options that use the infinitive ("to have told").

Now, let's analyze the meaning. The speaker is angry now because of an action that happened (or didn't happen) in the past. The other person did not tell the truth, and that action is completed. To show that a past action is the cause of a present feeling, we use the perfect gerund: $\mathrm{having}+\mathrm{past}\mathrm{participle}$.

Since the action was not done, we add "not" before the gerund. The correct form is therefore "not having told".

Let's evaluate the options:

• not having told: This is a perfect active gerund ("having told"). It is correct because "she" is the one who should have performed the action of telling. She did not tell (active voice).
• not to have told: This uses an infinitive ("to have told"), which cannot follow a preposition like "for".
• not to have been told: This is an infinitive in the passive voice ("to have been told"). It implies she was not *told* the truth by someone else, which changes the meaning. The sentence is about her not *telling* the truth.
• not having been told: This is a perfect passive gerund ("having been told"). Like the previous option, it incorrectly uses the passive voice, suggesting she did not receive the truth.

Final Answer: The most appropriate word to fill in the blank is not having told.
The complete sentence is: "I'm angry with her for not having told me the truth."

Related Topics & Formulae

Gerunds: A gerund is the -ing form of a verb used as a noun (e.g., swimming is fun, I am good at cooking).

Perfect Gerund (Formula): $\mathrm{having}+\mathrm{past}\mathrm{participle}$ (e.g., having eaten, having finished). This form is used to refer to a past action.

Rule: Prepositions (e.g., for, about, of, at, with) are followed by a noun or a gerund, never an infinitive.