Geometry

Question Analysis

This question involves the concept of vertical angles within a geometric diagram of intersecting lines.

 

Key Concept Explanation

Vertical angles are pairs of non - adjacent angles formed when two lines intersect. They share a common vertex and have equal measures.

 

Step - by - Step Solution

1. First, locate the vertex of ∠GKF, which is point K.

2. Observe the intersecting lines at point K. The lines IF and JG intersect here.

3. Look for the angle that is opposite to ∠GKF at vertex K. The angle ∠JKI is formed by the same two intersecting lines (IF and JG) and is opposite ∠GKF at vertex K.

 

Option Analysis

A.∠EKF: This angle shares a common side with ∠GKF, so it's an adjacent angle, not a vertical one.

B.∠JKI: Since it is formed by the same intersecting lines as ∠GKF and is opposite to it at the common vertex K, it is the vertical angle.

C.∠GKH: It has a common side with ∠GKF, making it adja...