1. The problem states that two vertical angles are formed by intersecting lines, with one angle measuring 145° and the opposite angle measuring (2x + 15)°. 2. Vertical angles are always equal, so we set the expressions equal to each other: $$145 = 2x + 15$$ 3. To solve for $x$, subtract 15 from both sides: $$145 - 15 = 2x + \cancel{15} - \cancel{15}$$ $$130 = 2x$$ 4. Now divide both sides by 2 to isolate $x$: $$\frac{130}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ $$65 = x$$ 5. Therefore, the value of $x$ is 65.