Use 'livid' for extreme anger, more than just 'mad' or 'upset.' It emphasizes a very strong feeling. He was livid after being falsely accused.
Pro Tip 2/3
Not for Minor Annoyance
'Livid' is inappropriate for slight irritation or mild annoyance; it's for serious instances. She wasn't just irritated, she was livid about the betrayal.
Pro Tip 3/3
Expressive Contexts
Use 'livid' when you want to convey a vivid image of someone's anger in storytelling. The character was livid, his fists clenched and eyes blazing.