1. **State the problem:** We are given two parallel lines $m$ and $n$ cut by a transversal, and two angles: one is $(10x+1)^\circ$ below the top line $m$, and the other is $(5x+29)^\circ$ above the bottom line $n$. We need to find the value of $x$. 2. **Identify the relationship:** Since $m \parallel n$, the angles given are alternate interior angles, which are congruent. 3. **Set up the equation:** $$ 10x + 1 = 5x + 29 $$ 4. **Solve for $x$:** Subtract $5x$ from both sides: $$ 10x + 1 - \cancel{5x} = 5x + 29 - \cancel{5x} \implies 5x + 1 = 29 $$ Subtract 1 from both sides: $$ 5x + 1 - 1 = 29 - 1 \implies 5x = 28 $$ Divide both sides by 5: $$ \frac{5x}{\cancel{5}} = \frac{28}{\cancel{5}} \implies x = \frac{28}{5} = 5.6 $$ 5. **Final answer:** $$ x = 5.6 $$