Geometry

Question Analysis

This question is centered around the concept of vertical angles within a geometric 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 ∠GKI, which is point K.

2. Observe the intersecting lines at point K. Here, the lines IF and JG intersect at K.

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

 

Option Analysis

A.∠FKJ: Since it is formed by the same intersecting lines as ∠GKI and is opposite to it at the common vertex K, it is the vertical angle.

B.∠GKF: This angle shares a common side with ∠GKI, so it is an adjacent angle, not a vertical one.

C.∠IKJ: It also shares a common side with ∠GKI, making it adjacent rather than verti...