From the image, we are given two parallel lines $m \parallel n$ and a transversal $t$. The angles formed are $(7x + 9)^\circ$ and $(9x - 5)^\circ$. Because $m \parallel n$, these angles are corresponding angles, which means they are equal.

We can set up the equation:

$7x + 9 = 9x - 5$

Solving for $x$:

1. Subtract $7x$ from both sides: $9 = 2x - 5$
2. Add 5 to both sides: $14 = 2x$
3. Divide by 2: $x = 7$

Therefore, the value of $x$ is $7$.

Would you like a step-by-step explanation or have any questions about this solution?

Related Questions:

1. What are corresponding angles, and how do they behave when lines are parallel?
2. How do you identify alternate interior angles and determine their relationships?
3. What would change if the angles given were supplementary instead of equal?
4. Can you explain the properties of transversals with respect to parallel lines?
5. How would you solve for $x$ if the angles were $(7x + 9)^\circ$ and $(180 - (9x - 5))^\circ$?

Tip:

When dealing with parallel lines cut by a transversal, remember that corresponding angles are always equal, while alternate interior angles are also equal.