Question

which of the following transformations carry this regular polygon onto itself? image of a regular pentagon with a vertical line of symmetry l rotation of 72° counterclockwise rotation of 36° counterclockwise rotation of 120° clockwise reflection across l

Explanation:

Step1: Identify polygon type

The figure is a regular pentagon (5 sides).

Step2: Find rotational symmetry angle

For n sides, rotational symmetry angle is $\frac{360^\circ}{n} = \frac{360^\circ}{5} = 72^\circ$. So rotations by multiples of $72^\circ$ work.

Step3: Check reflection symmetry

Line $l$ is a vertical axis through a vertex and the midpoint of the opposite side, which is a line of symmetry for a regular pentagon.

Answer:

rotation of 72° counterclockwise, reflection across l