Question

1. what is the smallest angle of rotation needed to rotate this figure to create an identical figure?

Explanation:

Step1: Determine the number of congruent parts

The figure has 8 congruent parts.

Step2: Calculate the angle of rotation

The formula for the smallest angle of rotation \( \theta=\frac{360^{\circ}}{n}\), where \(n\) is the number of congruent parts. Here \(n = 8\), so \(\theta=\frac{360^{\circ}}{8}=45^{\circ}\)

Answer:

\(45^{\circ}\)