Question: What is the measure of $$\angle x$$? Angles are not necessarily drawn to scale. Lines $$L N$$ and $$M O$$ intersect at point $$O$$. Angle $$M O N$$ is labeled $$133$$ degrees and angle $$M O L$$ is labeled $$X$$ degrees.
1. **State the problem:** We need to find the measure of $$\angle x$$, which is $$\angle M O L$$, given that $$\angle M O N = 133^\circ$$ and lines $$L N$$ and $$M O$$ intersect at point $$O$$.
2. **Identify the relationship:** When two lines intersect, the opposite (vertical) angles are equal, and the adjacent angles are supplementary (sum to $$180^\circ$$).
3. **Apply the supplementary angle rule:** Since $$\angle M O N$$ and $$\angle M O L$$ are adjacent angles formed by intersecting lines, they satisfy:
$$
\angle M O N + \angle M O L = 180^\circ
$$
4. **Substitute the known value:**
$$
133^\circ + x = 180^\circ
$$
5. **Solve for $$x$$:**
$$
x = 180^\circ - 133^\circ
$$
$$
x = 47^\circ
$$
6. **Final answer:**
$$\boxed{47^\circ}$$ is the measure of $$\angle x$$.