@GeometryPuzzles Oops, it seems I was wrong.🙄
Regardless of whether the curvature is positive or negative (spherical/cylindrical, saddle-shaped), the sum of the angles of the scissors around the intersection of lines on a non-Euclidean surface is always 360 degrees. Same as Euclidean.
@TheFigen_ This is a game that GEISHA play with customers.
The loser drinks alcohol as a penalty. GEISHA are used to this game, so they never lose to customers except as a performance.
This is a technique to get customers drunk quickly. Of course, the customers enjoy it too.