AngleFBC and AngleCBG are supplements, AngleDBG and AngleDBF are supplements, and AngleCBG Is-congruent-to AngleDBF.

4 lines are shown. A horizontal line with points F, B, G intersects a vertical line with points A, B, E at point B and forms a right angle. Another diagonal line with points D, B, C intersects the other 2 lines at point B between angle F B E and angle A B G. A fourth line intersects 3 lines at points A, C, G.
By the congruent supplements theorem, what can you conclude?

AngleCBG Is-congruent-to AngleDBG
AngleFBC Is-congruent-to AngleDBG
AngleCBG is supplementary to AngleDBF.
AngleFBC is supplementary to AngleDBG.

Based on the congruent supplements theorem which says that two angles are that are supplements of the same angle are congruent, therefore: ∠FBC ≅ ∠DBG.

What is the Congruent Supplements Theorem?

The congruent supplements theorem states that when two angles are congruent or supplements of the same angle, therefore, the two angles can be proven to be congruent angles.

Therefore, from the information given, we can conclude based on the congruent supplements theorem that: ∠FBC ≅ ∠DBG.

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