By the term Rotational Symmetry, we Mean the Position of the figure at which the figure looks same after rotation. Let us first look at the figure of a Circle. We say that the circle is a curved closed curve, which can be drawn by joining all the dots which are at the equal distance from the center.
Now we look at the rotational symmetry circle. By rotational symmetry we mean the new position of the figure after the rotation at certain angle, where it looks exactly same as the original figure. For this let us first rotate the circle by 1 degree and we observe that the circle is still symmetrical with respect to rotation. Similarly if we rotate the circle by 1 degree every time, the circle is at the rotational symmetry. In another situation, we say that if the circle is rotated by any other angle say 0.5 degree, again the same situation arises. Thus we find that even by rotating the circle by 0.5 degrees, the circle will be at the rotational symmetry.
This check can be tried for any of the angle measure. Now the question arises, that what is the order of rotational symmetry of the circle. We say that the circle is at the rotational symmetry, when it is rotated by any angle. Thus we cannot find the order of rotational symmetry of the circle. Thus we say that the order of rotational symmetry of the circle is infinite.
Thus we conclude that the circle is a special figure which can have any angle of rotational symmetry and thus we cannot find the order of rotation for this figure. By this we mean that the circle if rotated by any measure of the angle is at the rotational symmetry, so it is symmetrical at every angle rotation. Thus we say that the angle of rotation of the circle can be any angle and the order of rotation of the circle is infinite.