Problem 2. Given a right triangle $ABC$, with a right angle at vertex $C$ and the angle at vertex $B$ equal to $20^{\circ}$. The angle bisector of $\measuredangle BAC$ intersects the leg $BC$ at point $D$, and the angle bisector of $\measuredangle ABC$ intersects the leg $AC$ at point $F$. From points $D$ and $F$, perpendiculars are drawn to the hypotenuse and intersect the hypotenuse at points $M$ and $N$. Calculate $\measuredangle MCN$.