1. **State the problem:** Given two parallel lines $m \parallel n$ cut by a transversal $t$, find the value of $x$ when the angles $(5x - 8)^\circ$ and $(4x + 8)^\circ$ are given as shown. 2. **Identify the relationship:** Since $m \parallel n$ and $t$ is a transversal, the angles given are alternate interior angles, which are congruent. 3. **Set up the equation:** $$5x - 8 = 4x + 8$$ 4. **Solve for $x$:** Subtract $4x$ from both sides: $$5x - \cancel{4x} - 8 = \cancel{4x} + 8$$ $$x - 8 = 8$$ Add 8 to both sides: $$x - \cancel{8} + \cancel{8} = 8 + 8$$ $$x = 16$$ 5. **Conclusion:** The value of $x$ is $16$. This means the angles are equal, confirming the property of alternate interior angles when lines are parallel.