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We are given that ∠1 and ∠2 are vertical angles, and the measures of these angles are expressed as:

- m∠1 = (6x - 26)°
- m∠2 = (5x + 6)°

Since ∠1 and ∠2 are vertical angles, they are congruent, meaning:

\[
m∠1 = m∠2
\]

This gives us the equation:

\[
6x - 26 = 5x + 6
\]

### Solving for \( x \):

1. Subtract \( 5x \) from both sides:
   \[
   6x - 5x - 26 = 5x - 5x + 6
   \]
   \[
   x - 26 = 6
   \]

2. Add 26 to both sides:
   \[
   x - 26 + 26 = 6 + 26
   \]
   \[
   x = 32
   \]

Now that we know \( x = 32 \), we can substitute it back into the expression for m∠2:

\[
m∠2 = 5x + 6 = 5(32) + 6 = 160 + 6 = 166°
\]

Thus, the measure of ∠2 is **166°**.

Would you like a more detailed explanation or have any questions? Here are some related questions to explore further:

1. What is the sum of the measures of angles on a straight line?
2. How do we classify pairs of angles such as vertical, complementary, and supplementary?
3. What is the relationship between the measures of complementary and supplementary angles?
4. How can we apply the concept of congruent angles in triangle problems?
5. Can the concept of vertical angles be extended to three-dimensional geometry?

**Tip:** Always double-check whether angles are vertical or adjacent to determine if they are congruent or supplementary.

∠1 and ∠2 are vertical angles. If m∠1 = (6x - 26)° and m∠2 = (5x + 6)°, then find the measure of ∠2.

This problem involves solving for the measure of a vertical angle using linear equations. It is based on the Vertical Angles Theorem, where the measures of the angles are set equal to each other. Suitable for students in Grades 8-10.

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