https://file.aiquickdraw.com/mathbot/file/17254074924220j9yn2y1.jpg

The image shows a geometric problem involving angles formed by intersecting lines. There are three angles marked: one angle is \( x \), another is \( 2 \), and the third is \( 8x - 45 \).

Given that these angles are adjacent and form a straight line, their sum should be equal to \( 180^\circ \).

Let's write the equation to represent this:

\[
x + 2 + (8x - 45) = 180
\]

Now, let's solve this equation step by step:

1. Combine like terms:
\[
x + 8x + 2 - 45 = 180
\]
\[
9x - 43 = 180
\]

2. Add 43 to both sides to isolate the term with \( x \):
\[
9x = 223
\]

3. Divide both sides by 9:
\[
x = \frac{223}{9} \approx 24.78
\]

So, \( x \) is approximately \( 24.78^\circ \).

If you have any questions or want further details, feel free to ask!

### Related Questions:
1. What are the exact measures of the other angles in the diagram?
2. What happens if the angle sum doesn't equal 180° in a geometric problem?
3. How can you verify the solution by substituting \( x \) back into the original angles?
4. Can you solve the same problem using a different method, such as the exterior angle theorem?
5. What are the properties of angles that add up to a straight line?

### Tip:
Always double-check your work by substituting your answer back into the original equation to ensure it satisfies all conditions.

Given the angles x, 2, and 8x - 45 formed by intersecting lines, find the value of x.

This problem involves finding the value of x given three angles that form a straight line. The solution uses basic algebraic manipulation and the Linear Pair Theorem to arrive at the answer. Suitable for students in Grades 8-10.

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