Question

Line Z Y also contains points E and G. A line is drawn from point E to point F, and then to point X. Another line is drawn from F to G to form triangle E F G.
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.

Answer 1

To analyze the relationships of the angles in triangle EFG and the corresponding angles formed by point F and line ZY, we will consider each of the statements you provided:

1. **∠XFG is an interior angle of ΔEFG.**
- **False.** ∠XFG is not an angle of triangle EFG; it involves point X which is outside of triangle EFG.

2. **∠EFG is an interior angle of ΔEFG.**
- **True.** ∠EFG is one of the angles that form triangle EFG.

3. **∠FEZ is an exterior angle of ΔEFG.**
- **True.** Since line ZY contains point E and line segment EF is part of triangle EFG, ∠FEZ is formed by extending line segment EF.

4. **∠YGE is an exterior angle of ΔEFG.**
- **True.** Similarly, extending EG beyond point G forms ∠YGE as an exterior angle.

5. **∠EGF and ∠FGY are supplementary angles.**
- **True.** ∠EGF and ∠FGY are adjacent angles that lie on a straight line, so they sum up to 180 degrees.

6. **∠FEG and ∠FGE are supplementary angles.**
- **False.** ∠FEG and ∠FGE are angles within triangle EFG and do not sum to 180 degrees.

Based on the analysis, the true statements are:

- ∠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.