1. **State the problem:** We are given two expressions, $3x - 71$ and $x + 20$, which are labeled near intersections of a diagonal line with two parallel lines. We want to find the value of $x$ such that these expressions are equal, assuming they represent corresponding segments or angles. 2. **Set up the equation:** Since the expressions correspond to the same measure, set them equal: $$3x - 71 = x + 20$$ 3. **Solve for $x$:** Subtract $x$ from both sides: $$3x - \cancel{x} - 71 = \cancel{x} + 20 - x$$ $$2x - 71 = 20$$ Add 71 to both sides: $$2x - 71 + 71 = 20 + 71$$ $$2x = 91$$ Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{91}{\cancel{2}}$$ $$x = \frac{91}{2} = 45.5$$ 4. **Interpretation:** The value of $x$ that makes the two expressions equal is $45.5$. **Final answer:** $$x = 45.5$$