1. **State the problem:** Given two parallel lines $m \parallel n$ and a transversal $t$, find the value of $x$ when the angles formed are $(5x + 23)^\circ$ and $(6x - 4)^\circ$. 2. **Use the property of corresponding angles:** When two parallel lines are cut by a transversal, corresponding angles are equal. So, $$5x + 23 = 6x - 4$$ 3. **Solve the equation:** Subtract $5x$ from both sides: $$\cancel{5x} + 23 = \cancel{5x} + 6x - 4 \implies 23 = x - 4$$ Add 4 to both sides: $$23 + 4 = x - 4 + 4 \implies 27 = x$$ 4. **Final answer:** $$\boxed{27}$$ Thus, the value of $x$ is 27.