Question

1. I was angry that the door was locked.

2. I was angry the door was locked.
3. I was angry because the door was locked.
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Can we omit 'that' as in #2?
Does #1 mean #3?
In Sentence 1, Is "that the ...' an adverbial clause?

Answer 1

! and 3 are best. Yes, "because..." and "that..." are adverbials, modifying "was angry".

#2 is okay in casual speech -- it would be understood -- but not in formal writing.