Question

7 from unit 1, lesson 16 in the figure shown, identify any angles of rotation that create symmetry.

Explanation:

Step1: Count the number of equal - parts

The figure is divided into 8 equal - parts.

Step2: Calculate the angle of rotation

The formula for the angle of rotation for a symmetric figure divided into \(n\) equal - parts is \(\theta=\frac{360^{\circ}}{n}\). Here \(n = 8\), so \(\theta=\frac{360^{\circ}}{8}=45^{\circ}\).
The angles of rotation that create symmetry are \(45^{\circ}\times k\), where \(k = 1,2,\cdots,8\). That is \(45^{\circ},90^{\circ},135^{\circ},180^{\circ},225^{\circ},270^{\circ},315^{\circ},360^{\circ}\)

Answer:

The angles of rotation that create symmetry are \(45^{\circ},90^{\circ},135^{\circ},180^{\circ},225^{\circ},270^{\circ},315^{\circ},360^{\circ}\)