1. **State the problem:** We are given two angles formed by a transversal crossing two parallel lines. The angles are $ (85 - 2x)^\circ $ and $ (93 - 4x)^\circ $. We need to solve for $ x $. 2. **Identify the relationship:** Since the lines are parallel and the transversal crosses them, the angles $ (85 - 2x)^\circ $ and $ (93 - 4x)^\circ $ are corresponding angles or alternate interior angles, which are equal. 3. **Set up the equation:** $$ 85 - 2x = 93 - 4x $$ 4. **Solve for $ x $:** Subtract 85 from both sides: $$ \cancel{85} - 2x - \cancel{85} = 93 - 4x - 85 $$ which simplifies to $$ -2x = 8 - 4x $$ Add $4x$ to both sides: $$ -2x + 4x = 8 - 4x + 4x $$ which simplifies to $$ 2x = 8 $$ Divide both sides by 2: $$ \frac{\cancel{2}x}{\cancel{2}} = \frac{8}{2} $$ which simplifies to $$ x = 4 $$ 5. **Answer:** The value of $ x $ is $ 4 $.