Question

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

Explanation:

Step1: Recall the congruent supplements theorem

If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.
We know that \(\angle FBC\) and \(\angle CBG\) are supplements (\(\angle FBC+\angle CBG = 180^{\circ}\)), \(\angle DBG\) and \(\angle DBF\) are supplements (\(\angle DBG+\angle DBF=180^{\circ}\)), and \(\angle CBG\cong\angle DBF\).

Step2: Apply the congruent supplements theorem

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

Answer:

\(\angle FBC\cong\angle DBG\) (the second option)