<Tri-2025-2265>, hint

Suppose a triangle ABC such that <A>60, <B=60, <C<60, Then a>b>c

In triangle BA'C' <A'BC'=180  and A'C'=a+c.

Similarly B'C'<b+c, A'B'<a+b. Thus A'C'(=a+c)>B'C'(<b+c), A'B'C' cannot be equilateral