The question asks about angles that are vertical to each other. Vertical angles are pairs of angles that are formed by two intersecting lines, and they are opposite each other. Vertical angles are always congruent.

Given Options:

1. ∠16 and ∠9
2. ∠9 and ∠14
3. ∠10 and ∠12
4. ∠7 and ∠12

Steps to Solve:

1. Analyze the diagram for intersecting lines and identify pairs of opposite angles.
2. Note the relationships:
   • At the top intersection (lines forming angles ∠3, ∠4, ∠11, ∠12), ∠11 and ∠12 are not vertical because they are adjacent. Instead:
     • Vertical pairs: ∠3 and ∠12, ∠4 and ∠11.
   • At the bottom intersection (lines forming angles ∠7, ∠8, ∠15, ∠16), vertical pairs include:
     • ∠7 and ∠16, ∠8 and ∠15.
   • At the middle intersection (lines forming ∠9, ∠10, ∠13, ∠14), vertical pairs include:
     • ∠9 and ∠14, ∠10 and ∠13.

Answer:

The correct pair of vertical angles from the given options is ∠9 and ∠14.

Would you like more explanation or details?

Related Questions:

1. What are adjacent angles and how are they different from vertical angles?
2. How can you determine complementary or supplementary angle pairs in similar setups?
3. What are alternate interior angles in parallel line diagrams?
4. How do intersecting lines help identify congruent angles?
5. Can vertical angles occur with curved or non-linear figures?

Tip:

When analyzing angles in diagrams, look for intersecting lines as a starting point to identify vertical, adjacent, and corresponding angle relationships.