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Given that ∠A and ∠B are vertical angles, their measures are equal. The equation for the angles is:

\[
m∠A = m∠B
\]

We are given:
\[
m∠A = 5x + 25 \quad \text{and} \quad m∠B = 16x - 22
\]

Since they are vertical angles:

\[
5x + 25 = 16x - 22
\]

Now, solve for \(x\):

1. Subtract \(5x\) from both sides:
   \[
   25 = 11x - 22
   \]

2. Add 22 to both sides:
   \[
   47 = 11x
   \]

3. Divide both sides by 11:
   \[
   x = \frac{47}{11} = 4.27
   \]

Thus, the value of \(x\) is approximately **4.27** (rounded to the nearest hundredth).

Would you like further details on the solution?

Here are some follow-up questions to enhance understanding:
1. How are vertical angles defined?
2. Can you find the measure of ∠A using the value of \(x\)?
3. What would happen if the angles were complementary instead of vertical?
4. Can you express the angle measures if the relationship between ∠A and ∠B was different (e.g., supplementary)?
5. How can you verify the solution is correct after finding \(x\)?

**Tip:** Always check the units and context when solving angle problems to ensure accuracy.

Given that ∠A and ∠B are vertical angles, and m∠A = 5x + 25 and m∠B = 16x - 22, what is the value of x? Round your answer to the nearest hundredth if necessary.

Learn how to solve for x in an equation involving vertical angles, where m∠A = 5x + 25 and m∠B = 16x - 22. This problem involves algebra and geometry concepts, suitable for students in Grades 7-10. Follow the step-by-step solution and understand the key concepts behind vertical angles and linear equations.

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