Try lerping. lerp(a, b, x) Linear interpolation of a to b by x. Calculates a + x * (b - a).
So a is your starting point, b is your target, and x is the amount between the two values (0-1 scale)
For your case, object.angle is a, angle(object.x,object.y,mouse.x,mouse.y) is b, and you can choose anything between 0 and 1 which determines how much you want to move towards the target every tick.
Note that this will never actually reach your target value unless you round() the value. And even then only when your c value is more than 0.5.