Exquisite Archangel and it's replacement effect
Hi,
That's covered by this rule:
400.6. If an object would move from one zone to another, determine what event is moving the object. If the object is moving to a public zone and its owner will be able to look at it in that zone, its owner looks at it to see if it has any abilities that would affect the move. If the object is moving to the battlefield, each other player who will be able to look at it in that zone does so. Then any appropriate replacement effects, whether they come from that object or from elsewhere, are applied to that event. If any effects or rules try to do two or more contradictory or mutually exclusive things to a particular object, that object’s controller—or its owner if it has no controller—chooses which effect to apply, and what that effect does. (Note that multiple instances of the same thing may be mutually exclusive; for example, two simultaneous “destroy” effects.) Then the event moves the object.
When state-based actions are checked, there are two things trying to move the Archangel: its trying to move it to exile since you would lose the game, and it's trying to move to the graveyard since it has lethal damage marked on it. The controller of the Archangel gets to choose which effect to apply and where that card ends up, so they get to choose if it ends up in exile or if it ends up in the graveyard.
Nathan Long
Magic Rules NetRep