Geometry

Question Analysis

This question involves the concept of Vertical angles.

 

Key Concept Explanation:

Vertical angles are congruent. When two lines intersect, vertical angles are the pairs of opposite angles, and they have equal measures.

 

Step-by-Step Solution

1. Observe the given figure of intersecting lines.

2. Look for the angle that forms a vertical - angle pair with ∠4.

3. Notice that ∠1 and ∠4 are vertical angles.

 

Option Analysis

A.∠1: Since ∠1 and ∠4 are vertical angles, they are congruent.

B.∠5: It is adjacent to ∠4, so it is not congruent to ∠4.

C.∠6: It has no vertical - angle relationship with ∠4 and is not congruent.