Question

1. which statement about vertical angles in this diagram is true?

options:

• $\angle 1$ and $\angle 3$ are vertical angles
• $\angle 4$ and $\angle 6$ are vertical angles
• $\angle 5$ and $\angle 8$ are vertical angles
• $\angle 2$ and $\angle 4$ are vertical angles

Explanation:

Vertical angles are formed when two lines intersect, and they are opposite each other, sharing a common vertex but no common side. Let's analyze each option:

• For ∠1 and ∠3: They are adjacent angles, not vertical angles.
• For ∠4 and ∠6: These angles are not formed by the intersection of two lines in a way that makes them vertical (they are on different intersecting line pairs).
• For ∠5 and ∠8: They are adjacent angles, not vertical angles.
• For ∠2 and ∠4: These angles are formed by the intersection of two lines, are opposite each other, and share a common vertex with no common side, so they are vertical angles.

Answer:

D. ∠2 and ∠4 are vertical angles (assuming the last option is D; if the options are labeled differently, adjust the label but the angle pair is ∠2 and ∠4)