KöMaL 2024 B5362

In triangle $ABC$ it is given that $\angle BAC=50^\circ$ and $\angle ABC=70^\circ$. On sides $AC$ and $BC$ points $E$ and $D$ are chosen satisfying the following properties: $\angle ABE =\angle BAD = 30^\circ$. Let $M$ denote the intersection point of line segments $AD$ and $BE$. Find the magnitude of angles $\angle ACM$ and $\angle BED$.