https://file.aiquickdraw.com/mathbot/file/1726007405124v4ce5vil.jpg

The image shows two intersecting lines with angles marked as \((9e - 8)^\circ\) and \((8e + 2)^\circ\).

Since these angles are vertically opposite angles, they are equal. Therefore, we can set the two expressions equal to each other:

\[
9e - 8 = 8e + 2
\]

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

1. Subtract \(8e\) from both sides:

\[
9e - 8e - 8 = 2
\]

2. Simplify:

\[
e - 8 = 2
\]

3. Add 8 to both sides:

\[
e = 10
\]

So, the value of \(e\) is \(10\).

Would you like more details or have any questions? Here are some related questions:

1. How do you solve for variables when dealing with vertically opposite angles?
2. What are the properties of intersecting lines?
3. How would the solution change if one of the angles was given in radians?
4. What is the geometric proof for vertically opposite angles being equal?
5. How can this concept be applied to solving problems in parallel lines with a transversal?

**Tip**: Vertically opposite angles are always equal because they are formed by two intersecting lines, making them congruent pairs!

Solve for the value of e given the angles (9e - 8)° and (8e + 2)° are vertically opposite.

Learn how to solve for the variable 'e' in a problem involving vertically opposite angles. We set the expressions (9e - 8)° and (8e + 2)° equal, solve the linear equation, and find e = 10. Suitable for Grades 7-9.

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