To solve the problem, let's analyze the image you provided. Let me extract the math problem from it and provide the solution.

The problem asks to find the value of $x$ given that lines $m$ and $n$ are parallel, and we have the following angles:

1. One angle is labeled $(2x - 10)^\circ$,
2. The other is $(65 - x)^\circ$.

Since $m$ and $n$ are parallel, these two angles are corresponding angles, so they are equal. This gives us the equation:

$2x - 10 = 65 - x$

Step-by-step Solution:

1. Start by isolating $x$: $2x + x = 65 + 10$

   $3x = 75$

2. Divide both sides by 3: $x = 25$

Final Answer:

$x = 25$

Would you like a detailed explanation of the geometric properties used, or do you have any other questions?

Here are 5 related questions for practice:

1. If the angles were supplementary instead of equal, what would the equation look like?
2. What are alternate interior angles, and how are they used in similar problems?
3. How would the solution change if $m$ and $n$ were not parallel?
4. Can this problem be solved geometrically without equations? How?
5. What other properties of parallel lines can be used to solve similar problems?

Tip:

Always verify whether the given angles are equal or supplementary when working with parallel lines, as this determines your setup equation.