Question

which of the following transformations carry this regular polygon onto itself? image of a square rotation of 72° counterclockwise rotation of 60° counterclockwise rotation of 90° counterclockwise rotation of 120° clockwise

Explanation:

Step1: Identify the polygon

The figure is a square (regular quadrilateral), so the number of sides \( n = 4 \).

Step2: Determine rotational symmetry angle

For a regular \( n \)-sided polygon, the smallest angle of rotation that maps it onto itself is \( \frac{360^\circ}{n} \). For \( n = 4 \), this is \( \frac{360^\circ}{4}=90^\circ \). So a rotation of \( 90^\circ \) (clockwise or counterclockwise) will carry the square onto itself. Rotations of \( 72^\circ \) (for \( n = 5 \)), \( 60^\circ \) (for \( n = 6 \)), and \( 120^\circ \) (for \( n = 3 \)) do not match the square's rotational symmetry.

Answer:

rotation of \( 90^\circ \) counterclockwise