1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are labeled as $5x + 6$ degrees and $8x - 39$ degrees. 2. **Identify the relationship:** Since the lines are parallel and the angles are corresponding angles, they are equal. 3. **Set up the equation:** $$5x + 6 = 8x - 39$$ 4. **Solve for $x$:** Subtract $5x$ from both sides: $$\cancel{5x} + 6 = 8x - \cancel{5x} - 39 \implies 6 = 3x - 39$$ Add 39 to both sides: $$6 + 39 = 3x - 39 + 39 \implies 45 = 3x$$ Divide both sides by 3: $$\frac{45}{\cancel{3}} = \frac{3x}{\cancel{3}} \implies 15 = x$$ 5. **Find the angle measures:** Substitute $x=15$ into each expression: $$5x + 6 = 5(15) + 6 = 75 + 6 = 81$$ $$8x - 39 = 8(15) - 39 = 120 - 39 = 81$$ 6. **Conclusion:** The value of $x$ is 15, and both angles measure 81 degrees, confirming they are equal as expected for corresponding angles.