1. The problem states that $\angle 1$ and $\angle 2$ are vertical angles, and their measures are given as $m\angle 1 = (7x - 9)^\circ$ and $m\angle 2 = (6x + 11)^\circ$. We need to find the value of $x$. 2. Vertical angles are always equal. So, we set their measures equal: $$7x - 9 = 6x + 11$$ 3. To solve for $x$, subtract $6x$ from both sides: $$7x - \cancel{6x} - 9 = \cancel{6x} + 11$$ which simplifies to $$x - 9 = 11$$ 4. Next, add 9 to both sides: $$x - 9 + 9 = 11 + 9$$ which simplifies to $$x = 20$$ 5. Therefore, the value of $x$ is $20$.