Question

which angles are supplementary to each other? ∠bgd and ∠agb; ∠cge and ∠agb; ∠bgc and ∠agb; ∠fgb and ∠bgd

Explanation:

Step1: Recall definition of supplementary angles

Supplementary angles are two angles whose sum is 180 degrees. They form a linear - pair (a straight - line).

Step2: Analyze each option

For $\angle BGD$ and $\angle AGB$, they do not form a linear - pair.
For $\angle CGE$ and $\angle AGB$, they do not form a linear - pair.
For $\angle BGC$ and $\angle AGB$, they do not form a linear - pair.
For $\angle FGB$ and $\angle BGD$, they form a linear - pair since they are adjacent angles and their non - common sides form a straight line. So $\angle FGB+\angle BGD = 180^{\circ}$, and they are supplementary.

Answer:

$\angle FGB$ and $\angle BGD$