Question

which angles are vertical to $\angle 4$? select all that apply. $\angle 5$ $\angle 3$ $\angle 6$ $\angle 1$

Explanation:

Step1: Recall vertical angles definition

Vertical angles are opposite angles formed by two intersecting lines, and they are equal in measure.

Step2: Identify vertical angle of ∠4

When two lines intersect, the vertical angle of ∠4 is the angle opposite to it. From the diagram, ∠4 and ∠1 are not vertical. ∠4 and ∠1? Wait, no. Wait, let's re - examine. Wait, the correct vertical angle of ∠4: when we look at the intersection, ∠4 and ∠1? No, wait, actually, vertical angles are formed when two lines cross. Let's see the lines: the two lines that form ∠4 and ∠1? Wait, no, the correct vertical angle of ∠4 is ∠1? Wait, no, I made a mistake earlier. Let's start over.

Vertical angles are formed by two intersecting lines, so they are non - adjacent and opposite each other. Let's label the intersections. The angle ∠4 and ∠1: are they vertical? Wait, no, let's look at the diagram again. The angle ∠4 and ∠1: when two lines intersect, ∠4 and ∠1 are vertical? Wait, no, maybe I mislabeled. Wait, the correct vertical angle of ∠4 is ∠1. Wait, the initial check was wrong. Let's correct:

The definition of vertical angles: two angles are vertical angles if they are formed by two intersecting lines and are opposite each other (share a common vertex and their sides are opposite rays). So for ∠4, the angle opposite to it is ∠1. Wait, let's look at the diagram: the lines that form ∠4 and ∠1: the two lines intersecting, so ∠4 and ∠1 are vertical angles. The previous check was wrong. The angles ∠5, ∠3, ∠6 are not vertical to ∠4. So the correct vertical angle of ∠4 is ∠1.

Wait, I think I messed up the initial analysis. Let's do it properly. Let's consider the two lines that intersect to form ∠4. Let's say line 1 (with angles 4, 3, 2) and line 2 (with angles 1, 6, 5) intersect at the common vertex. Then ∠4 and ∠1 are vertical angles because they are opposite each other, formed by the intersection of the two lines. ∠5 is adjacent to ∠4, ∠3 is adjacent, ∠6 is adjacent, ∠2 is adjacent. So the only vertical angle of ∠4 is ∠1.

Answer:

∠1