1. **Stating the problem:** We are given several angle relationships involving expressions with $x$ and specific angle measures. We need to find the value of $x$ in the first problem where two adjacent angles are labeled $2x$ and $4x$. 2. **Formula and rules:** Adjacent angles on a straight line sum to $180^\circ$. This is because they form a linear pair. 3. **Set up the equation:** $$2x + 4x = 180$$ 4. **Simplify the equation:** $$6x = 180$$ 5. **Solve for $x$:** $$x = \frac{180}{6}$$ 6. **Cancel common factors:** $$x = \cancel{\frac{180}{6}} = 30$$ 7. **Answer:** The value of $x$ is $30$ degrees. This completes the solution for the first problem involving angles $2x$ and $4x$ adjacent on a straight line.