Question

the figure below has rotational symmetry. ° is the smallest possible rotation that results in the figure being mapped onto itself. answer attempt 2 out of 2

Explanation:

Step1: Understand rotational symmetry

Rotational symmetry is when a figure can be rotated and still look the same. For a figure with $n$ - fold rotational symmetry, the smallest rotation angle $\theta$ that maps the figure onto itself is given by $\theta=\frac{360^{\circ}}{n}$, where $n$ is the number of times the figure can be mapped onto itself during a full - 360 - degree rotation.

Step2: Determine the number of times the figure can map onto itself

This figure can be rotated 4 times to map onto itself during a 360 - degree rotation ($n = 4$).

Step3: Calculate the smallest rotation angle

Using the formula $\theta=\frac{360^{\circ}}{n}$, substituting $n = 4$, we get $\theta=\frac{360^{\circ}}{4}=90^{\circ}$.

Answer:

$90$