2003 Cayley Problem 25

\angle BAC is said to be "laceable" if distinct points X_1, X_2, \ldots, X_{2n} can be found so that

- X_{2k-1} is on AC for each value of k, - X_{2k} is on AB for each value of k, and - AX_1 = X_1X_2 = X_2X_3 = \cdots = X_{2n-1}X_{2n} = X_{2n}A.

For example, the angle 20^\circ is laceable, as shown. The number of laceable acute angles, whose sizes in degrees are integers, is

\textbf{(A)}\ 3\quad \textbf{(B)}\ 4\quad \textbf{(C)}\ 5\quad \textbf{(D)}\ 6\quad \textbf{(E)}\ 7

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.