\section*{Problem 15}

\(\mathrm{ABC}\) is equilateral. \(\mathrm{A}\) line parallel to \(\mathrm{AC}\) meets \(\mathrm{AB}\) at \(\mathrm{M}\) and \(\mathrm{BC}\) at \(\mathrm{P}\). \(\mathrm{D}\) is the center of the equilateral triangle BMP. E is the midpoint of AP. Find the angles of DEC.

\section*{Answer}

\(\mathrm{D}=60^{\circ}, \mathrm{E}=90^{\circ}\)