Question

for each figure below, determine if it has rotational symmetry. if it does, give the smallest angle of rotation needed for the figure to appear unmoved. rotational symmetry? ⚫ yes ○ no angle? 72° rotational symmetry? ⚫ yes ○ no angle? □°

Explanation:

Step1: Identify the polygon type

The right figure is a regular octagon (8 - sided polygon).

Step2: Calculate the smallest rotation angle

For a regular \( n \) -sided polygon, the smallest angle of rotational symmetry is given by the formula \( \frac{360^{\circ}}{n} \). Here, \( n = 8 \), so we calculate \( \frac{360^{\circ}}{8} \).
\( \frac{360^{\circ}}{8}=45^{\circ} \)

Answer:

\( 45 \)