In the diagram below, a regular hexagon is inscribed in a circle. One of the triangles formed by connecting the center of the circle to two adjacent vertices of the hexagon is highlighted. What is the measure of each angle of this highlighted triangle?

[asy]
size(100);
import graph;
draw(Circle((0,0),2));
pair A = dir(0), B = dir(60), C = dir(120), D = dir(180), E = dir(240), F = dir(300);
draw(A--B--(0,0)--A--cycle);
draw((0,0)--C); draw((0,0)--D); draw((0,0)--E); draw((0,0)--F);
label("A", A, dir(A));
label("B", B, dir(B));
label("C", C, dir(C));
label("D", D, dir(D));
label("E", E, dir(E));
label("F", F, dir(F));
label("O", (0,0), S);
\end{asy] Let's think step by step and output the final answer within \boxed{}.
user