One angle tells the other angle

Let $\Delta ABC$ be an acute angled triangle with $\angle C=60^\circ$ . Perpendiculars $AA_1$ and $BB_1$ are drawn from point $A$ and $B$ to the sides $BC$ and $AC$ , respectively. Let $M$ be the midpoint of $AB$ .

What is the value of $\frac{\angle A_1MB_1}{\angle A_1CB_1}$ ?