If the figure has rotational symmetry, find the angle of rotation about the center that results in an image that matches the original figure.
The figure shows a design made with large and small flowers.The figure is a design with 15 identical flowers arranged in a circle in three groups of 5. The three groups are equally spaced apart on the circle, and the 5 flowers in each group are equally spaced. The are three groups of 3 small flowers that form a segment between the center and flower circle. In each segment group, there is another small flower on the counterclockwise side of the small flower just inside the flower circle.
(1 point)
Responses
90°
90°
120°
120°
210°
210°
no rotational symmetry
The figure does not have rotational symmetry because there is no angle of rotation that results in an image that matches the original figure.
To find the angle of rotation that results in an image that matches the original figure, we need to identify the rotational symmetry of the figure.
In this case, we can see that the figure is symmetrical about the center. Each group of flowers is equally spaced apart on the circle, and the flowers within each group are equally spaced as well.
Since there are three groups of flowers, we can rotate the figure by 360°/3 = 120° to get an image that matches the original figure.
Therefore, the angle of rotation about the center that results in an image that matches the original figure is 120°.