Question

1. determine the minimum rotation (in degrees) which will carry the following figure onto itself (where all sides and vertices will match up). round to the nearest tenth if necessary.

22.5
360
180
60
45
90

Explanation:

Step1: Recall rotational - symmetry formula

For a regular polygon with \(n\) sides, the minimum angle of rotation \(\theta\) that maps the polygon onto itself is given by \(\theta=\frac{360^{\circ}}{n}\), where \(n\) is the number of sides of the polygon. However, we first need to count the number of sides of the given polygon. By counting the sides of the polygon in the figure, we find that \(n = 8\).

Step2: Calculate the minimum rotation angle

Substitute \(n = 8\) into the formula \(\theta=\frac{360^{\circ}}{n}\). So, \(\theta=\frac{360^{\circ}}{8}=45^{\circ}\).

Answer:

45