1. **State the problem:** We need to find the value of $x$ given a right triangle with a vertical leg labeled $3x + 6$ and a horizontal leg labeled $30$. 2. **Understand the problem:** The two right triangles share a common angle, so they are similar triangles. This means the ratios of corresponding sides are equal. 3. **Set up the proportion:** Since the triangles are similar, the ratio of the vertical leg to the horizontal leg in one triangle equals the ratio in the other. Here, the vertical leg is $3x + 6$ and the horizontal leg is $30$. 4. **Use the ratio:** Let the corresponding sides in the smaller triangle be $a$ and $b$. Then: $$\frac{3x + 6}{30} = \frac{a}{b}$$ Since the problem does not provide $a$ and $b$, we assume the ratio equals 1 (or the triangles are right triangles with legs in proportion). So: $$3x + 6 = 30$$ 5. **Solve for $x$:** $$3x + 6 = 30$$ Subtract 6 from both sides: $$3x = 24$$ Divide both sides by 3: $$x = 8$$ 6. **Answer:** The value of $x$ is $8$.