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Angela explains that she just knew that Eragon was a Rider.
Eragon tells her that Brom has died, and Angela says that it was Brom's fate to fail at all of his tasks (including loving a woman), save one—killing Morzan. Still, he succeeded at a pretty important task.
Eragon's curious: What's Angela doing in Tronjheim?
Angela says she likes to be "wherever important events are occurring" (54.24), and, anyway, Solembum would have come here with or without her. She likes his company.
Eragon catches her up on the events she's missed out on.
Angela warns Eragon to be careful about trusting Murtagh, and also to watch out for that nasty Shade character.
It turns out that a Shade is actually someone who is possessed by an evil spirit—forever.
So what's Angela doing way up here, above Tronjheim?
She's hiding out. When she first got there, a bunch of magic users tried to get her to join their secret group, especially the Twins. She got annoyed and so she's hiding out here to avoid them.
Eragon asks if the Twins scanned her mind like they did to him, but she says that they wouldn't dare try. She's been coming here since they were just knee-high to a grasshopper.
And that's that. Angela ushers Eragon out, making him promise not to tell anyone that she's here.