<Polygon-2025-277>, hint

Let angles A=C=E =P, B=D=F=Q

Since 3(P+Q)=720, P+Q=240., Suppose BA  extended and EF extended  meet  at U.

Since <A+<F=240, <AUF=60. Hence lines AB, CD, EF meet at  the vertices of an 

equilateral triangle(UVW) and point P is the  incenter of UVW