1. The problem states that we have a triangle with angles labeled as $9x$, $30^\circ$, and $33^\circ$. We need to find the value of $x$. 2. Recall that the sum of the interior angles of any triangle is always $180^\circ$. This is the key formula we will use: $$9x + 30 + 33 = 180$$ 3. Combine the known angle measures: $$9x + 63 = 180$$ 4. Subtract 63 from both sides to isolate the term with $x$: $$9x = 180 - 63$$ $$9x = 117$$ 5. Divide both sides by 9 to solve for $x$: $$x = \frac{117}{9}$$ $$x = 13$$ 6. Therefore, the value of $x$ is $13^\circ$. This means the angle labeled $9x$ is $9 \times 13 = 117^\circ$, and the triangle's angles add up correctly to $180^\circ$.