Question

if a figure has 90° rotational symmetry, what other symmetries must it have? the figure must also have the following rotational symmetry(ies) □° (do not include the degree symbol in your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Understand rotational symmetry

If a figure has \(n^{\circ}\) rotational symmetry, then it also has rotational symmetries of \(k\times n^{\circ}\), where \(k\) is a positive integer such that \(k\times n^{\circ}\leq360^{\circ}\).
Given \(n = 10\).

Step2: Find multiples of \(10\) less than or equal to \(360\)

Let \(k = 2\), then \(2\times10=20\); \(k = 3\), then \(3\times10 = 30\); \(k=4\), then \(4\times10=40\); \(k = 6\), then \(6\times10=60\); \(k=9\), then \(9\times10 = 90\); \(k = 12\), then \(12\times10=120\); \(k=18\), then \(18\times10=180\); \(k= 36\), then \(36\times10=360\)

Answer:

\(20,30,40,60,90,120,180,360\)