Question

1. name an angle vertical to \\( \angle d g e \\).

a. \\( \angle d g f \\)
b. \\( \angle i g j \\)
c. \\( \angle i g e \\)
d. \\( \angle h g e \\)

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines. They are opposite each other.

Step2: Analyze each option

• Option A: $\angle DGF$ is adjacent to $\angle DGE$, so it is not a vertical angle.
• Option B: $\angle IGJ$ is formed by different line intersections and is not opposite to $\angle DGE$.
• Option C: $\angle IGE$ is opposite to $\angle DGE$ as they are formed by the intersection of two lines and are non - adjacent.
• Option D: $\angle HGE$ is adjacent to $\angle DGE$, so it is not a vertical angle.

Answer:

C. $\angle IGE$