https://file.aiquickdraw.com/mathbot/file/1725927123050x87bemci.jpg

In the image, we are given two intersecting lines, and two angles are formed by these intersecting lines:

- One angle is labeled as \( (8w + 8)^\circ \)
- The other is labeled as \( (9w - 5)^\circ \)

Since the angles are opposite each other (vertical angles), they are congruent, meaning their measures are equal.

To solve for \( w \), we can set the two expressions equal to each other:

\[
8w + 8 = 9w - 5
\]

Now let's solve this equation step by step:

1. Subtract \( 8w \) from both sides to get the variables on one side:
   \[
   8w + 8 - 8w = 9w - 5 - 8w
   \]
   Simplifying:
   \[
   8 = w - 5
   \]

2. Add 5 to both sides to isolate \( w \):
   \[
   8 + 5 = w - 5 + 5
   \]
   Simplifying:
   \[
   13 = w
   \]

Thus, the value of \( w \) is \( \boxed{13} \).

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. What are vertical angles, and why are they always equal?
2. If the angles were complementary or supplementary, how would the equation change?
3. How can you solve for unknowns if the angles are part of a triangle?
4. What happens if one of the angles was given in terms of another variable, not \( w \)?
5. How does the concept of linear pairs relate to vertical angles?

**Tip:** Always check whether angles formed by intersecting lines are vertical or adjacent, as this helps determine how to set up equations.

Solve for the value of w given two vertical angles: (8w + 8)° and (9w - 5)°.

Learn how to solve for w by setting two vertical angles equal: (8w + 8)° = (9w - 5)°. This problem involves algebraic expressions and the vertical angles theorem. Suitable for students in Grades 7-9.

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