Angular speed is how fast the central angle changes in respect to time. Below you will see an angle that is changing by $\theta$ distance.

With this in mind, you can now define the angular speed of any given angle.

$$angular\ speed=\frac { central\quad angle }{ time }$$ You can then abstract this out even one more step by using $\theta$ angle with $t$ time.

$$angular\ speed=\frac { \theta }{ t }$$

Remember all that $\theta$ is the value of the arc divided by the radius. See "How to find theta of any given angle?"