Question

which angles are vertical to ∠6? select all that apply. ∠1 ∠2 ∠3 ∠8

Explanation:

Step1: Recall vertical angles definition

Vertical angles are opposite angles formed by two intersecting lines, they are equal and share a common vertex.

Step2: Analyze ∠6's vertical angle

Looking at the intersection where ∠6 is, the two intersecting lines form ∠6 and ∠8? Wait, no, wait. Wait, the lines: the left transversal and the horizontal line. Wait, ∠6 and ∠8? No, wait, when two lines intersect, vertical angles are opposite. Wait, the angle vertical to ∠6: let's see the intersection of the left slant line and the horizontal line. The angles at that intersection: ∠6, ∠7, ∠5, ∠8. So vertical angles: ∠6 and ∠8? Wait no, wait ∠6 and ∠8? Wait, no, ∠6 and ∠8: no, when two lines intersect, the vertical angle of ∠6 should be ∠8? Wait, no, let's label: the two lines (horizontal and left slant) intersect, creating four angles: ∠6, ∠7 (top left), ∠5 (bottom right), ∠8 (top right). So vertical angles: ∠6 and ∠8? Wait, no, ∠6 is bottom left, ∠8 is top right? Wait, no, vertical angles are opposite. So ∠6 (bottom left) and ∠8 (top right)? No, wait, ∠6 and ∠8: no, ∠6 and ∠8 are adjacent? Wait, no, maybe I messed up. Wait, the correct vertical angle for ∠6: when two lines intersect, the vertical angle is the one opposite, so ∠6 and ∠8? Wait, no, let's see: the horizontal line and the left slant line intersect. So ∠6 and ∠8: are they vertical? Wait, ∠6 is at the bottom left, ∠8 is at the top right. Wait, no, ∠6 and ∠8: no, the vertical angle of ∠6 should be ∠8? Wait, no, maybe the diagram: let's re-express. The horizontal line is from left to right. The left slant line goes from bottom left to top right? Wait, no, the arrows: the horizontal line has left and right arrows. The left slant line has an arrow going down left and up right. So the intersection: ∠6 is bottom left (between left slant down and horizontal left), ∠7 is top left (between left slant up and horizontal left), ∠5 is bottom right (between left slant down and horizontal right), ∠8 is top right (between left slant up and horizontal right). So vertical angles: ∠6 and ∠8? No, ∠6 and ∠8 are not vertical. Wait, ∠6 and ∠8: no, ∠6 and ∠8 are adjacent? Wait, no, vertical angles are opposite. So ∠6 (bottom left) and ∠8 (top right) – no, that's not. Wait, maybe I made a mistake. Wait, the other intersection: the right slant line and horizontal line. But ∠6 is at the left intersection. Wait, the problem is which angles are vertical to ∠6. So at the left intersection (horizontal and left slant), the vertical angle of ∠6 is ∠8? Wait, no, ∠6 and ∠8: no, ∠6 and ∠8 are supplementary? Wait, no, vertical angles are equal. Wait, maybe the correct vertical angle is ∠8? Wait, but in the options, ∠8 is an option. Wait, but the initial check marks were wrong. Wait, the correct vertical angle for ∠6 is ∠8? Wait, no, let's recall: vertical angles are formed by two intersecting lines, so ∠6 and ∠8: are they formed by the same two lines? Yes, the horizontal and left slant. So ∠6 and ∠8: are they vertical? Wait, ∠6 is (horizontal below, slant left below), ∠8 is (horizontal above, slant left above). So they are opposite, so vertical angles. So the angle vertical to ∠6 is ∠8. Wait, but the other options: ∠1, ∠2, ∠3 are at the other intersection. So the correct answer should be ∠8. Wait, the initial check marks were wrong. So let's correct.

Answer:

∠8