3 [ Angles subtended by equal arcs and equal chords]

The vertex of an angle measuring $70^{\circ}$ is the origin of a ray that forms angles of $30^{\circ}$ and $40^{\circ}$ with its sides. Perpendiculars are dropped from a point $M$ on this ray to the sides of the angle, with the feet of the perpendiculars being $A, B$, and $C$. Find the angles of triangle $A B C$.

#