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Verify and prove that, how and why "Formula to find the Order of rotation" is :

(360^{°}/Angle of rotation).

{Please don't provide any web - link or certified answer... I want only experts answer}

The number of times a figure fits into itself in one complete rotation is called the order of rotational symmetry.

If A° is the smallest angle by which a figure is rotated so that rotated from fits onto the original form, then the order of rotational symmetry is given by 360°/A° [A° < 180°]

It can be only varified

**Rectangle (clockwise)**

We observe that while rotating the figure through 360°, it attains original from two times i.e., it looks exactly the same at two positions. Thus, we say that the rectangle has a rotational symmetry of order 2.

**Equilateral triangle (clockwise):**

We observe that at all 3 positions, the triangle looks exactly the same when rotated about its center by 120°.

**Letter B (clockwise):**

We observe that only at one position the letter looks exactly the same after taking one complete rotation.

**Windmill (anticlockwise):**

We observe that if we rotate it by one – quarter, at 4 positions, it looks exactly the same. Therefore, the order of rotational symmetry is 4.

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