Question

is the smallest possible rotation that results in the figure being mapped onto itself. you must answer all questions above in order to submit.

Explanation:

Step1: Identify the number of rotational symmetries

The figure has 3 - fold rotational symmetry. To find the smallest rotation that maps the figure onto itself, we use the formula for the angle of rotation of a regular - shaped object with \(n\) rotational symmetries, which is \(\theta=\frac{360^{\circ}}{n}\).

Step2: Calculate the angle of rotation

Here, \(n = 3\) (since the figure can be rotated 3 times to map onto itself). So, \(\theta=\frac{360^{\circ}}{3}=120^{\circ}\).

Answer:

\(120^{\circ}\)