To find the measure of $\angle x$, I would need additional information about the geometric context of the angle. Here are some common cases that could apply:

1. Triangle Angles: If $\angle x$ is part of a triangle, we could use the property that the sum of angles in a triangle is $180^\circ$.
2. Parallel Lines and Transversals: If $\angle x$ is formed by parallel lines intersected by a transversal, we could use alternate interior angles or corresponding angles properties.
3. Circle Properties: If $\angle x$ is an inscribed angle or a central angle of a circle, there are special properties that could help determine its measure.
4. Polygon Angles: If $\angle x$ is part of a polygon, we could use the sum of interior angles or other polygon-specific properties.
5. Right Angles or Complementary Angles: If $\angle x$ is complementary or supplementary to a given angle, we could use that to find its measure.

Could you please provide more details about $\angle x$ or share an image of the problem? This will allow me to give a precise solution.

---

Would you like more examples or further details? Here are some related questions that might help clarify:

1. What is the sum of angles in a triangle, and how can it be applied?
2. How do alternate interior angles work with parallel lines and transversals?
3. What is an inscribed angle in a circle, and what is its property?
4. How can we determine the angle sum of an $n$-sided polygon?
5. What is the difference between complementary and supplementary angles?

Tip: Remember, geometric figures often include hidden relationships, so examine diagrams closely for parallel lines, symmetry, or special angle types.