<Polygon-2025-278>, hint

Consider a regular pentagon ABCDE inscribed in a circle O .

While C,D are fixed, pull A inside O to make <A be almost 180 (max angle among A,B,C,D,E)

then at least one of B, E are pushed out of O. Adjust <B smaller than <E.

At this moment <C, <D become bigger than 108, because B, E are outside O.

Thus <A is max and <B is min