Word that means "to complete another person's sentence"?

Example:

"She doesn't eat meat. I think she's a ..." he trailed off.

"Vegetarian?" I [...].

The only word I could think of is interjected. But I think it's wrong, because it implies interruption, while the example implies addition.

What's a more appropriate word?


Solution 1:

"She doesn't eat meat. I think she's a ..." he trailed off.

"Vegetarian?" I volunteered.

volunteer

1.2 [reporting verb] Say or suggest something without being asked: [with object]: ‘it never paid to volunteer information’

[with direct speech]: ‘‘Her name’s Louise,’ Christina volunteered’

Oxford Dictionaries

Solution 2:

Note: I do not find this answer better than the previous, I just want to make an extended comment with some formatting.

posit:

  1. to place, put, or set.
  2. to lay down or assume as a fact or principle; postulate.

"Vegetarian?" I posited.

I like this verb because you use both meanings. The connotation can be "fill in the blank," at least to me.

But most examples online are seemingly drawn from people talking about the scientific method—only postulating, not placing—so someone tell me how idiomatic this is.