Outside perimeter = AH+DH+DG+BG+BF+EF+EJ+CJ+CI+AI = 50

Pentagon perimeter = HG+GH+FJ+JI+IH = 30

Adding these two equations

(AH+DH+DG+BG+BF+EF+EJ+CJ+CI+AI) + (HG+GH+FJ+JI+IH) = 50 + 30

Rearranging them,

(AH+HG+BG)+(BF+FJ+CJ)+(CI+IH+DH)+(DG+GF+EF)+(EJ+AI+JI) = 80

that is AB+BC+CD+DE+EA=80