1. **State the problem:** We are given two angles formed by a transversal crossing two parallel lines. The angles are $ (15x + 8)^\circ $ and $ (9x + 26)^\circ $. We need to find the value of $ x $. 2. **Identify the relationship:** Since the lines are parallel and the angles are on the same side of the transversal, these angles are consecutive interior angles, which are supplementary. This means their measures add up to 180 degrees. 3. **Write the equation:** $$ (15x + 8) + (9x + 26) = 180 $$ 4. **Simplify the equation:** $$ 15x + 8 + 9x + 26 = 180 $$ $$ 24x + 34 = 180 $$ 5. **Solve for $ x $:** $$ 24x = 180 - 34 $$ $$ 24x = 146 $$ $$ x = \frac{146}{24} = \frac{73}{12} \approx 6.0833 $$ 6. **Final answer:** $$ x = \frac{73}{12} $$