1998 Gauss 8 Problem 19

A regular pentagon has all sides and angles equal. If the shaded pentagon is enclosed by squares and triangles, as shown, what is the size of angle x?

\textbf{(A)}\ 75^\circ\quad \textbf{(B)}\ 108^\circ\quad \textbf{(C)}\ 90^\circ\quad \textbf{(D)}\ 60^\circ\quad \textbf{(E)}\ 72^\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 Gauss contests here.