Question

$\angle fbc$ and $\angle cbg$ are supplements, $\angle dbg$ and $\angle dbf$ are supplements, and $\angle cbg \cong \angle dbf$.
by the congruent supplements theorem, what can you conclude?
$\bigcirc$ $\angle cbg \cong \angle dbg$
$\bigcirc$ $\angle fbc \cong \angle dbg$
$\bigcirc$ $\angle cbg$ is supplementary to $\angle dbf$.
$\bigcirc$ $\angle fbc$ is supplementary to $\angle dbg$.

Explanation:

Step1: Recall Congruent Supplements Theorem

The theorem states: If two angles are supplementary to congruent angles, then the two angles are congruent.

Step2: Map given to theorem

We know:

1. $\angle FBC$ is supplementary to $\angle CBG$
2. $\angle DBG$ is supplementary to $\angle DBF$
3. $\angle CBG \cong \angle DBF$

So $\angle FBC$ and $\angle DBG$ are supplementary to congruent angles.

Step3: Apply theorem

By the congruent supplements theorem, $\angle FBC \cong \angle DBG$.

Answer:

$\boldsymbol{\angle FBC \cong \angle DBG}$ (Option B)