To solve for $x$, we need to use the fact that the angles labeled $(15x + 8)^\circ$ and $(9x + 26)^\circ$ are corresponding angles. Corresponding angles are equal when two parallel lines are intersected by a transversal, which seems to be the case in this diagram.

Given:

$15x + 8 = 9x + 26$

Solving for $x$:

1. Subtract $9x$ from both sides: $6x + 8 = 26$
2. Subtract 8 from both sides: $6x = 18$
3. Divide by 6: $x = 3$

Thus, the solution is $x = 3$.

Would you like more details or have any questions?

Related Questions:

1. How do corresponding angles help in solving geometry problems?
2. What are alternate interior angles, and when are they used?
3. What are the properties of parallel lines when intersected by a transversal?
4. How can we verify if two lines are parallel using angle measurements?
5. What other types of angles are created when two parallel lines are intersected by a transversal?

Tip:

Remember, when two lines are intersected by a transversal, look for corresponding, alternate interior, or supplementary angles to help solve for unknown values!