Parallel Lines X 3F9F30

1. **State the problem:** We are given two parallel lines $m$ and $n$ cut by a transversal $t$. We need to find the value of $x$ given the angles $(8x-2)^\circ$ and $(9x-14)^\circ$. 2. **Identify the relationship between the angles:** Since $m \parallel n$ and $t$ is a transversal, the angles $(8x-2)^\circ$ and $(9x-14)^\circ$ are corresponding angles. 3. **Use the property of corresponding angles:** Corresponding angles are equal when lines are parallel. So, $$8x - 2 = 9x - 14$$ 4. **Solve the equation:** $$8x - 2 = 9x - 14$$ Subtract $8x$ from both sides: $$\cancel{8x} - 2 = \cancel{8x} + 9x - 14 \Rightarrow -2 = x - 14$$ Add $14$ to both sides: $$-2 + 14 = x - 14 + 14 \Rightarrow 12 = x$$ 5. **Final answer:** $$\boxed{12}$$