1. **State the problem:** We need to find the value of $x$ in a hexagon where the interior angles are given as $x^\circ$, $120^\circ$, $156^\circ$, $145^\circ$, $(x+9)^\circ$, and one right angle ($90^\circ$). 2. **Formula for sum of interior angles of a polygon:** The sum of interior angles of an $n$-sided polygon is given by: $$\text{Sum} = (n-2) \times 180^\circ$$ For a hexagon ($n=6$), $$\text{Sum} = (6-2) \times 180^\circ = 4 \times 180^\circ = 720^\circ$$ 3. **Set up the equation:** The sum of all given angles must equal $720^\circ$: $$x + 120 + 156 + 145 + (x + 9) + 90 = 720$$ 4. **Simplify the equation:** $$x + (x + 9) + 120 + 156 + 145 + 90 = 720$$ $$2x + 9 + 511 = 720$$ $$2x + 520 = 720$$ 5. **Solve for $x$:** $$2x = 720 - 520$$ $$2x = 200$$ $$x = \frac{200}{2}$$ $$x = 100$$ 6. **Final answer:** $$\boxed{100}$$