Question

which angles are congruent to each other?

Explanation:

Step1: Recall the definition of congruent angles

Congruent angles are angles that have the same measure.

Step2: Analyze each option

• For $\angle FGB$ and $\angle FGA$: $\angle FGB+\angle FGA = 180^{\circ}$ (they are supplementary, not necessarily congruent).
• For $\angle BGD$ and $\angle FGB$: These are vertical angles. By the vertical - angles theorem, vertical angles are congruent.
• For $\angle FGB$ and $\angle AGB$: $\angle FGB+\angle AGB

eq$ a known fixed non - variable relationship (they are not congruent).

• For $\angle BGD$ and $\angle DGE$: $\angle BGD+\angle DGE

eq$ a known fixed non - variable relationship (they are not congruent).

Answer:

$\angle BGD$ and $\angle FGB$