Question

1. which reason is the justification for the statement that angle 1 ≅ angle 4? alternate exterior angles theorem definition of parallel lines vertical angles theorem given

Explanation:

Step1: Recall the Vertical Angles Theorem

Vertical angles are formed when two lines intersect. The Vertical Angles Theorem states that vertical angles are congruent.

Step2: Check the relationship between ∠1 and ∠4

∠1 and ∠2 are vertical angles (congruent), ∠2 and ∠3 are alternate - interior angles (if lines \(n\) and \(p\) are parallel, they are congruent), ∠3 and ∠4 are vertical angles (congruent). But if we consider the direct relationship based on the theorem for the given pair \(\angle1\) and \(\angle4\) without going through the middle - angle steps (since \(\angle1\cong\angle2\), \(\angle2\cong\angle3\), \(\angle3\cong\angle4\) by vertical and alternate - interior angles, but the most direct theorem for a pair of angles formed by two intersecting lines is the vertical angles theorem when considering the overall structure of angle congruence justifications in geometry problems of this type).

Answer:

Vertical Angles Theorem