1. **Problem statement:** We are given a triangle with points K, L, M and a point N on segment KM. Angles are marked as follows: $\angle LKN = y^\circ$, $\angle LNM = 3y^\circ$, $\angle NM = x^\circ$, and $\angle LNM = 18^\circ$. We need to find the value of $x$. 2. **Analyze the given angles:** From the problem, $\angle LNM$ is given twice: once as $3y^\circ$ and once as $18^\circ$. This means: $$3y = 18$$ 3. **Solve for $y$:** $$y = \frac{18}{3} = 6$$ 4. **Use $y$ to find $x$:** Since $\angle LKN = y^\circ = 6^\circ$ and $\angle NM = x^\circ$, we need to find the relationship between $x$ and $y$. Given the problem's angle markings, $x = y$ (assuming $x$ corresponds to the same angle measure as $y$ or is equal to it based on the triangle's properties). 5. **Final answer:** $$x = 6$$ Thus, the value of $x$ is 6 degrees.