Question

which of the following transformations carry this regular polygon onto itself? image of a square rotation of 90° counterclockwise (checked) rotation of 36° counterclockwise (checked) rotation of 45° clockwise (checked) rotation of 40° counterclockwise (checked)

Explanation:

Step1: Identify the polygon

The figure is a square (4-sided regular polygon).

Step2: Find rotation symmetry angle

For n-sided regular polygon, minimal rotation angle = $\frac{360^\circ}{n}$. For square, $\frac{360^\circ}{4}=90^\circ$.

Step3: Check valid rotations

Only rotations by multiples of $90^\circ$ map square to itself. $90^\circ$ counterclockwise is a multiple of $90^\circ$.

Answer:

rotation of 90° counterclockwise