https://file.aiquickdraw.com/mathbot/file/1726850369453ry192fe3.jpg

The image depicts two intersecting lines forming vertical opposite angles. It appears that we are given the following information:

- One pair of opposite angles is labeled as \(16\) and \(12\).
- The other pair is labeled as \(15\) and \(y + 4\).

In a pair of vertically opposite angles, the angles are always equal. So, we can set up the following equation to solve for \(y\):

\[
15 = y + 4
\]

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

\[
y = 15 - 4 = 11
\]

Thus, the value of \(y\) is \(11\).

Would you like more details, or do you have any questions about this problem?

Here are 5 related questions to expand on this topic:

1. How do you know that vertically opposite angles are equal?
2. What are the properties of intersecting lines and their angles?
3. Can vertically opposite angles ever be supplementary?
4. How can you apply this knowledge to triangles or polygons?
5. What are corresponding and alternate angles in parallel lines?

**Tip:** Always remember that vertical angles are congruent, meaning they are equal in measure!

Solve for y by applying the vertically opposite angles theorem. In this geometry problem, intersecting lines form vertical angles, and we use algebra to find that y equals 11. This problem is suitable for students in Grades 6-8.

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