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This is a diagram involving angles formed by two intersecting lines. From the image, we observe two angles marked as \(3y^\circ\) and \(2y^\circ\), which are vertically opposite each other.

### Step-by-step solution:

1. **Vertically Opposite Angles:**
   Vertically opposite angles are equal, so we can set up the equation:
   \[
   3y = 2y
   \]
   This equation represents that both angles are equal since they are vertically opposite.

2. **Solving for \(y\):**
   To solve for \(y\), we simplify the equation:
   \[
   3y = 2y
   \]
   Subtract \(2y\) from both sides:
   \[
   y = 0
   \]

So, \(y = 0^\circ\).

However, based on the diagram and the context, there might be more to the problem that isn't captured by the initial interpretation. Would you like more details or have questions about this calculation?

Here are five related questions to consider:
1. What are vertically opposite angles, and why are they equal?
2. How are supplementary angles related to intersecting lines?
3. What other relationships might angles on a straight line exhibit?
4. Can you think of other geometric properties that apply to angles formed by parallel lines and transversals?
5. How would the solution change if the two lines were parallel?

**Tip:** Always remember that angles formed by intersecting lines have special properties like vertical angles being equal and adjacent angles summing to 180 degrees!

Calculate the value of y, showing all your working.

Learn how to solve for y in a geometry problem where two intersecting lines form vertically opposite angles. The problem involves applying the theorem of vertically opposite angles and understanding angle relationships. Suitable for Grades 7-9 students.

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