1. **Problem statement:** We are given two angles at point R on a straight line: one angle measures $3x$ degrees and the other measures $9x$ degrees. We need to find the value of $x$. 2. **Key concept:** Angles on a straight line add up to $180^\circ$. 3. **Set up the equation:** Since the two angles $3x$ and $9x$ are adjacent and form a straight line, their sum is: $$3x + 9x = 180$$ 4. **Simplify the equation:** $$12x = 180$$ 5. **Solve for $x$:** $$x = \frac{180}{12} = 15$$ 6. **Answer:** The value of $x$ is $15$ degrees.