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Given that ∠1 and ∠2 are vertical angles, we know that the measure of vertical angles is equal. Thus, the two expressions for the angles are set equal to each other:

\[
m∠1 = m∠2
\]

From the problem, we have:
\[
m∠1 = (2x + 16)^\circ \quad \text{and} \quad m∠2 = (6x - 8)^\circ
\]

Equating these two expressions, we get:
\[
2x + 16 = 6x - 8
\]

Now, let's solve for \(x\):

1. Subtract \(2x\) from both sides:
\[
16 = 4x - 8
\]

2. Add 8 to both sides:
\[
24 = 4x
\]

3. Divide by 4:
\[
x = 6
\]

Now that we know \(x = 6\), substitute this value back into the expression for \(m∠2\):

\[
m∠2 = (6x - 8)^\circ = (6(6) - 8)^\circ = (36 - 8)^\circ = 28^\circ
\]

Thus, the measure of ∠2 is **28°**.

Would you like further details or have any other questions?

Here are five related questions you can explore:
1. What are vertical angles, and why are they always equal?
2. How do we solve linear equations with variables on both sides?
3. What happens when two angles are complementary? How is this different from vertical angles?
4. Can vertical angles be supplementary, and under what conditions would that happen?
5. How would the solution change if the two angles were supplementary instead of equal?

**Tip:** Always double-check your work by substituting your solution back into the original equations.

∠1 and ∠2 are vertical angles. If m∠1 = (2x + 16)° and m∠2 = (6x - 8)°, find the measure of ∠2.

Learn how to solve for x when given two vertical angles. This step-by-step solution explains how to equate and solve the expressions (2x + 16)° and (6x - 8)° using basic algebra. Suitable for students in Grades 7-9.

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