1. **State the problem:** We are given two angles formed by intersecting lines: one angle is $3x$ degrees and the other is $30$ degrees. We want to find the value of $x$. 2. **Understand the relationship:** The two angles are supplementary because they form a straight line. Supplementary angles add up to $180^\circ$. 3. **Write the equation:** $$3x + 30 = 180$$ 4. **Solve for $x$:** Subtract $30$ from both sides: $$3x + \cancel{30} - \cancel{30} = 180 - 30$$ $$3x = 150$$ Divide both sides by $3$: $$\frac{3x}{\cancel{3}} = \frac{150}{\cancel{3}}$$ $$x = 50$$ 5. **Conclusion:** The value of $x$ is $50$ degrees. This means the angle $3x$ is $3 \times 50 = 150$ degrees, which together with the $30$ degrees angle sums to $180$ degrees, confirming the supplementary angle rule.