Geometry

Question Analysis

This question involves the concept of vertical angles in a figure with intersecting lines.

 

Key Concept Explanation

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

 

Step - by - Step Solution

1. Locate the vertex of ∠HKJ, which is point K.

2. Observe the intersecting lines at point K. The lines JG and EH intersect to form ∠HKJ.

3. Look for the angle that is opposite to ∠HKJ at vertex K. The angle ∠GKE is formed by the same two intersecting lines and is opposite ∠HKJ at vertex K.

 

Option Analysis

A.∠GKF: This angle is a part of ∠GKE. Since vertical angles are formed as complete non - adjacent pairs by the intersection of two lines, and ∠GKF doesn't meet the criteria of being the full angle opposite to ∠HKJ, it is incorrect.

B.∠EKJ: Shares a common side with ∠HKJ, it's an adjacent angle, not vertical.