Hey there!
So the Angel is what happens if you -lose- to Nadia in the game.
If you're aiming to lose, in general, you want to respond in a flustered way (or not at all) to her needling during the game, or ask inane/obvious questions when it's your turn to speak.
Also, while you can win when it's on, avoid the 'lucky' talent until after Nadia, as it does tilt things slightly in your favor.