Question

∠fbc and ∠cbg are supplements. ∠dbg and ∠dbf are supplements, and ∠cbg≅∠dbf. by the congruent supplements theorem, what can you conclude? ∠fbc≅∠dbg ∠cbg is supplementary to ∠dbf. ∠cbg≅∠dbg ∠fbc is supplementary to ∠dbg.

Explanation:

Step1: Recall congruent - supplements theorem

If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.

Step2: Identify given supplementary and congruent angles

We know that $\angle FBC$ and $\angle CBG$ are supplements, $\angle DBG$ and $\angle DBF$ are supplements, and $\angle CBG\cong\angle DBF$.

Step3: Apply the theorem

Since $\angle FBC$ and $\angle DBG$ are supplements of congruent angles ($\angle CBG$ and $\angle DBF$ respectively), by the congruent - supplements theorem, $\angle FBC\cong\angle DBG$.

Answer:

$\angle FBC\cong\angle DBG$