Re: all about although
Your two sentences about "angry" are correct but they suggest different things. Even though in both sentences the person was both smiling and angry, you have changed the emphasis on which one is more important - the smiling or the anger.
Originally Posted by mrbin
With the birthday party examples, the first is fine. The second is not. We might say "Although she didn't come, I did invite her to my party". The stress would be on the word "did" before "invite" as if you are trying to ensure that people understand that you didn't just forget about her. Again, the emphasis is on a different part of the situation in the two sentences.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.