Question

this image has rotational symmetry. what is the smallest number of degrees you need to rotate the image for it to look the same?

Explanation:

Step1: Analyze the image's symmetry

The image (a tomato slice - like figure with two identical parts) has rotational symmetry. A full rotation is \(360^\circ\). For a figure with \(n\) - fold rotational symmetry, the smallest angle of rotation is \(\frac{360^\circ}{n}\). Here, the figure looks the same when rotated by \(180^\circ\) (since it has two identical parts arranged symmetrically, so \(n = 2\)).

Step2: Calculate the smallest rotation angle

Using the formula for the angle of rotational symmetry \(\theta=\frac{360^\circ}{n}\), where \(n\) is the number of times the figure maps onto itself during a full rotation. For this figure, \(n = 2\) (because it has two congruent parts that are mirror - like in rotation). So \(\theta=\frac{360^\circ}{2}=180^\circ\).

Answer:

\(180\)