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.