2022 Cayley Problem 7

Points A, B, C, D, E, and F are evenly spaced around the circle with centre O, as shown. The measure of \angle AOC is

\textbf{(A)}\ 90^\circ\quad \textbf{(B)}\ 150^\circ\quad \textbf{(C)}\ 144^\circ\quad \textbf{(D)}\ 120^\circ\quad \textbf{(E)}\ 108^\circ

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.