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To solve for the measure of angle \( \angle 2 \) based on the given information, we can use the properties of vertical angles and corresponding angles in intersecting lines.

1. **Given:**
   - \( \angle 6 = 110^\circ \).

2. **Relationship between angles:**
   - \( \angle 6 \) and \( \angle 2 \) are **vertical angles**, meaning they are equal. Vertical angles are always congruent.

3. **Conclusion:**
   - Since vertical angles are congruent, \( m\angle 2 = m\angle 6 = 110^\circ \).

Thus, the measure of \( \angle 2 \) is **110°**.

Would you like further explanation or have any other questions?

### Related Questions:
1. What are vertical angles, and why are they always congruent?
2. How do alternate interior angles differ from corresponding angles in parallel lines?
3. Can we apply the same principle to find \( \angle 5 \) based on the diagram?
4. How can we use the concept of supplementary angles with intersecting lines?
5. What would the measure of \( \angle 4 \) be if \( \angle 6 = 110^\circ \)?

### Tip:
Always look for vertical and corresponding angles when dealing with intersecting lines, as they provide quick clues to solving for unknown angles.

What is the measure of angle 2 if angle 6 is 110°?

Learn how to solve for the measure of angle 2 using the Vertical Angle Theorem. In this problem, angle 6 is given as 110°, and the solution demonstrates that vertical angles are congruent, meaning angle 2 also measures 110°. Suitable for Grades 7-9.

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