Is the inner angle of a circle is 180? Is this true that polygon with infinitely many sides (which is a circle) 
all inner angles have 180 degrees (each) ?
 by this argument:

$$\frac{(m-2)\cdot180}{m}\space\space\space\Rightarrow\space\space\space180\space-\space\frac{360}{m}\space\space\space\space{\overrightarrow{_{m\rightarrow\infty}}}\space\space\space\space180$$


Is this true?
Technically not exactly 180, as a circle is a curve which doesn't technically have an angle, the best we can do is measure tangent lines. However the limit you have derived I agree with, and it makes sense. $180^0$ is a straight line, and for a circle these lines are hardly noticed because individually they all seem straight, just ever so slightly off the $180^0$ - this causes it to curve around in the fashion we see it do.
There's no polygon with infinitely many sides. A circle is not a polygon. It has no rectilinear parts, and hence no angles.