The congruent supplements theorem basically states that if we have two pairs of supplementary angles, say A and B are supplementary and C and D are supplementary and one of angle of each pair are congruent, say A congruent to C, then the other two are also congruent (say B congruent to D)
In our case, the angle A is the angle FBC, B is the angle CBG. C is the angle DBG and D is the angle DBF. Since B is congruent to D then A is congruent to C. So angle FBC is congruent to angle DBG, which is option 2
