Yeah, yeah, I know. And, normally, our Code is helpful with this question: the narrowest street frontage is the front, regardless of anything else. But, here's the trickier part.
The lot is square with the exact same frontage on both streets. Both streets are classified as residential streets (so no hierarchy exists). Dwellings are located on each adjoining lot facing each street.
The proposal is to move a historic structure and place it at an angle to the corner. Where are the setbacks, side yards, and rear yard?
State your rationale and be prepared to defend you answers.