https://file.aiquickdraw.com/mathbot/file/1726856290364nto6zffv.jpg

The diagram provided shows two intersecting lines, forming a pair of vertically opposite angles. The given angles are:

- \( (8z - 3)^\circ \)
- \( (7z + 7)^\circ \)

Since vertically opposite angles are always equal, we can set the two expressions equal to each other:

\[
8z - 3 = 7z + 7
\]

### Now, let's solve for \( z \):

1. Subtract \( 7z \) from both sides:
\[
8z - 7z - 3 = 7
\]
\[
z - 3 = 7
\]

2. Add 3 to both sides:
\[
z = 10
\]

Thus, the value of \( z \) is **10**.

Would you like more details on the solution or any clarifications?

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Here are 5 related questions:
1. How do you solve for \( z \) if the angles given were complementary?
2. What are supplementary angles, and how do they differ from vertically opposite angles?
3. Can vertically opposite angles ever be unequal? Why or why not?
4. How would the solution change if the expressions involved different operations (e.g., \( 8z + 3 \))?
5. What if the given angles were represented by other geometric shapes, like triangles or polygons?

**Tip:** Always remember that vertically opposite angles are equal when two lines intersect, regardless of the angle measures or their algebraic representations.

Solve for the value of z. The angles provided are (8z - 3)° and (7z + 7)°, which are vertically opposite angles.

Learn how to solve for z in a vertically opposite angles problem where the given expressions are (8z - 3)° and (7z + 7)°. This problem covers key algebraic concepts like solving linear equations and understanding geometry theorems. Suitable for Grades 6-8 students.

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