1. **Stating the problem:** We are given a circle with center $O$ and points $A, B, C, D, E$ on the circumference. We want to find the value of angle $x$ at vertex $C$ of triangle $AOC$. 2. **Understanding the problem:** Since $O$ is the center of the circle, segments $OA$ and $OC$ are radii of the circle and thus equal in length. 3. **Key property:** Triangle $AOC$ is isosceles with $OA = OC$. 4. **Using the isosceles triangle property:** The base angles opposite the equal sides are equal. So, the angles at $A$ and $C$ in triangle $AOC$ are equal. 5. **Given information:** The problem states an arrow from point $E$ indicating the number 25, which likely represents the measure of angle $x$. 6. **Conclusion:** Therefore, the value of angle $x$ is $25$ degrees. **Final answer:** $$x = 25$$