https://file.aiquickdraw.com/mathbot/file/1726234594296mh7vfuf3.jpg

The image shows two intersecting lines forming vertical angles. The angle on the left is given as \((5y - 16)^\circ\), and the angle on the right is \((4y + 6)^\circ\).

Since these are vertical angles, they are congruent, meaning they have the same measure. Therefore, we can set up the equation:

\[
5y - 16 = 4y + 6
\]

### Solving for \(y\):

1. Subtract \(4y\) from both sides:
   \[
   5y - 4y - 16 = 6
   \]
   \[
   y - 16 = 6
   \]

2. Add 16 to both sides:
   \[
   y = 6 + 16
   \]
   \[
   y = 22
   \]

### Verifying the angles:
- Substitute \(y = 22\) into the left angle: 
  \[
  5y - 16 = 5(22) - 16 = 110 - 16 = 94^\circ
  \]
- Substitute \(y = 22\) into the right angle:
  \[
  4y + 6 = 4(22) + 6 = 88 + 6 = 94^\circ
  \]

Both angles are \(94^\circ\), confirming that the solution is correct.

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Would you like further details or have any questions? Here are 5 related questions for deeper understanding:

1. What are vertical angles and how are they formed?
2. Can two vertical angles ever be supplementary? Why or why not?
3. What is the sum of the angles around the point of intersection?
4. How can you apply this concept to more complex geometry problems?
5. What happens if the angles were given in terms of different variables?

**Tip**: Always check your solution by substituting the variable back into the original expressions to verify the values are consistent.

Solve for y given the vertical angles: (5y - 16)° and (4y + 6)°.

Learn how to solve for y in the vertical angles problem with expressions (5y - 16)° and (4y + 6)°. This solution uses key algebraic concepts and the Vertical Angles Theorem, suitable for students in Grades 8-10.

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