Question

which statements regarding the diagram are true? check all that apply. □ ∠xfg is an interior angle of δefg. □ ∠efg is an interior angle of δefg. □ ∠fez is an exterior angle of δefg. □ ∠yge is an exterior angle of δefg. □ ∠egf and ∠fgy are supplementary angles. □ ∠feg and ∠fge are supplementary angles.

Explanation:

1. For $\angle XFG$: Interior angles of a triangle are formed by two sides of the triangle. $\angle XFG$ is formed by a side of the triangle (FG) and an extension (FX), so it's not an interior angle.
2. For $\angle EFG$: It is formed by two sides of $\triangle EFG$ (EF and FG), so it is an interior angle.
3. For $\angle FEZ$: An exterior angle is formed by one side of the triangle and the extension of another side. $\angle FEZ$ is formed by side EF and extension of EG (EZ), so it is an exterior angle.
4. For $\angle YGE$: $\angle YGE$ is a straight angle related to side EG, but it's not formed by a side of the triangle and an extension of another side in the context of $\triangle EFG$'s exterior angles (exterior angle at G would be related to FG and EG extension), so it's not an exterior angle of $\triangle EFG$.
5. For $\angle EGF$ and $\angle FGY$: They form a linear pair (they are adjacent and their non - common sides form a straight line), so they are supplementary (sum to $180^{\circ}$).
6. For $\angle FEG$ and $\angle FGE$: These are two interior angles of $\triangle EFG$. The sum of interior angles of a triangle is $180^{\circ}$, but supplementary angles sum to $180^{\circ}$ and are adjacent (or form a linear pair in some cases). These two angles are not supplementary as they are non - adjacent interior angles of a triangle.

Answer:

B. $\angle EFG$ is an interior angle of $\triangle EFG$, C. $\angle FEZ$ is an exterior angle of $\triangle EFG$, E. $\angle EGF$ and $\angle FGY$ are supplementary angles