Question

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

Explanation:

Step1: Identify the order of rotational symmetry

The figure has 4 identical - looking parts around a central point. The order of rotational symmetry \(n = 4\).

Step2: Calculate the angle of rotation

The formula to find the smallest angle of rotation \(\theta\) that maps a figure onto itself is \(\theta=\frac{360^{\circ}}{n}\). Substituting \(n = 4\) into the formula, we get \(\theta=\frac{360^{\circ}}{4}\).

Step3: Solve for the angle

\(\theta = 90^{\circ}\).

Answer:

90