Question

the figure below has rotational symmetry.
□° is the smallest possible rotation that results in the figure being mapped onto itself. try reset

Explanation:

Step1: Identify the figure's symmetry

The figure is a four - pointed star - like shape (a type of quadrilateral - based rotational symmetric figure). For a figure with rotational symmetry, the smallest angle of rotation (the order of rotational symmetry) can be found by dividing \(360^{\circ}\) by the number of times the figure can be mapped onto itself as it rotates through \(360^{\circ}\). This figure has 4 equal - looking "arms" or sections.

Step2: Calculate the smallest rotation angle

The formula for the smallest angle of rotational symmetry \(\theta\) is \(\theta=\frac{360^{\circ}}{n}\), where \(n\) is the order of rotational symmetry (the number of times the figure coincides with itself during a full rotation). Here, \(n = 4\) (since there are 4 identical parts). So \(\theta=\frac{360^{\circ}}{4}=90^{\circ}\).

Answer:

\(90\)