Angel is the introductory chapter of killer7, acting first and foremost as a tutorial of the game's core mechanics. Story-wise, Angel throws the player into a trial-by-fire kind of scenario; little to no context is given outside of several character names, and the player is mostly left to their own thoughts on what the game is about.
As mentioned above, Angel generally leaves the player alone for the most part in terms of context; while the Remnant Psyches give gameplay information and light details concerning the Heaven Smiles - along with an idea of what the Smith Syndicate is like, thanks to the Carrier Pigeon on the 3F stairway which gives basic information on all of them - little is mentioned about everything else.
Aside from this, Angel illustrates several other key points; i.e. the destructive nature and violence of the Heaven Smiles, the relationship between Harman Smith and Kun Lan, the personalities (and 'uses') of the Remnant Psyches, etc.
Somewhere in Seattle, a mysterious, suited man walks down a pavement in a city at nighttime; he's introduced as Garcian Smith. On the opposite site of the pavement walks another man who pulls out something that resembles a flyer and hands it over to Garcian as they cross paths and briefly exchange glances; before walking away, he's introduced as Christopher Mills. Garcian and Mills go their seperate ways, and after a brief section of walking, Garcian arrives at a building. He receives a call from Mills, who asks if he's arrived. Garcian comments on it as looking like a shithole, with Mills simply telling him that it's the building where "they all hang out." Mills continues, saying that his information states that there's fourteen of "them." Garcian asks if they're all to be killed on sight, but Mills notes that he should leave one alive so that they can find out who their leader is. In addition, he says that Garcian will recognize them at first sight, stating that they're visually different from the rest of the building's tenants. Garcian hangs up and enters the building. The assignment title card shows up shortly thereafter - Garcian's task is to destory the headquarters of the 'Heaven Smile' and capture their leader alive.
Upon entering the building's entrance hallway, Garcian spots a camera on one of the walls. Switching to the camera's point of view, Garcian suddenly morphs into Dan Smith - implying that he can change from persona to persona through television signals. Entering the lobby, Dan comes across someone who seems to be a survivor, who tells Dan that he should retreat since his friends were murdered by someone who looked "just like this," revealing themselves as a Heaven Smile. Dan kills the Smile and realizes that the information was wrong, as there's certainly more than fourteen Smiles - "those bastards are breeding."
After this encounter, Dan is introduced to a strange spirit who calls himself Vincel Dill Boris VII, Iwazaruscof... but tells Dan to call him Iwazaru in any case. Iwazaru introduces him to the concept of Harman's rooms; areas that act as (occasional) save spots, along with Iwazaru himself serving as a means of gaining information on the killer7 in the back of the room, and an ISZK television at the front allowing the killer7 to upgrade their abilities via serums made out of the thick blood acquirable by killing Smiles. Throughout most of the chapter, Iwazaru simultaneously discourages the killer7 from moving onwards, but also gives them information regarding the Smiles and about what to do.