1. **State the problem:** We need to find the value of $x$ that makes lines $A$ and $B$ parallel by using the property of alternate exterior angles. 2. **Recall the property:** Alternate exterior angles are equal when two lines are parallel. 3. **Set up the equation:** Given the angles are $10x$ degrees and $8x + 30$ degrees, set them equal: $$10x = 8x + 30$$ 4. **Solve for $x$:** Subtract $8x$ from both sides: $$10x - \cancel{8x} = \cancel{8x} + 30 - 8x$$ which simplifies to: $$2x = 30$$ Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{30}{\cancel{2}}$$ $$x = 15$$ 5. **Conclusion:** The value of $x$ that makes lines $A$ and $B$ parallel is $15$.