Cordelia: I finally get invited to a nice place with no mirrors and lots of curtains. Hey, you're a vampire!
Russell Winters: What? No, I'm not.
Cordelia: Are too!
Russell Winters: I don't know what you're talking about.
Cordelia: I'm from Sunnydale. We had our own Hellmouth. I think I know a vampire when... I'm... Alone with him... In his fortress-like home.
In The Dark - S1-E3
[Watching from on top of a building as Angel talks to a woman he just saved, Spike guesses what is being said.]
Spike: [as Rachel.] How can I thank you, you mysterious black-clad hunk of a night thing?
[as Angel.] No need, little lady, your tears of gratitude are enough for me. You see, I was once a badass vampire, but love and a pesky curse defanged me. Now I'm just a big, fluffy puppy with bad teeth. [Rachel reaches for Angel's head.] No, not the hair. Never the hair.
[as Rachel.] But there must be some way I can show my appreciation?
[as Angel.] No, helping those in need's my job, and working up a load of sexual tension and prancing away like a magnificent poof is truly thanks enough.
[as Rachel.] I understand. I have a nephew who is gay, so...
[as Angel.] Say no more. Evil's still afoot. And I'm almost out of that nancy-boy hair-gel I like so much. Quickly, to the Angel-mobile, away.
Angel: Can I come in?
Kate Lockley: Oh, that's right. You need to be invited in, don't you?
Angel: You've been doing your homework.
Kate Lockley: Want to quiz me? I'm just full of fun facts. For instance, I learned your friend has been in L.A. Before. Did you know that? Yeah, at least twice. Once in 1929 and again in 1963. Oh, and there was something in Boston in 1908. I think he was there, too.
Angel: So you believe me.
Kate Lockley: Yes, I believe you.
Angel: Good, because he's planning something else.
Kate Lockley: Angelus. Isn't that what he called you? Angelus. I looked it up, it's all right there. The demon with the face of an angel. A particularly brutal bastard by all accounts. Oh, and no, you can't come in.
Answer: Due to his epiphany, Angel basically had the 'true darkness' he worked so hard to reattain ripped away from him, like his soul was after sleeping with Buffy.