Final answer:
The answer identifies angles of rotation that produce symmetry in a flower based on radial symmetry, commonly 5-fold or 6-fold, corresponding to multiples of 72 or 60 degrees, respectively, and also mentions bilateral symmetry with a 180-degree rotation.
Step-by-step explanation:
The question involves identifying angles of rotation that correspond to symmetry in a flower. In mathematics, particularly geometry, symmetry refers to the property by which the shape of an object remains invariant under certain transformations, including rotation. Radial symmetry in flowers, such as sunflowers, exists when you can rotate the flower around its center by certain angles, and the flower appears unchanged.
The common types of radial symmetry are pentamerous (5-fold symmetry) and hexamerous (6-fold symmetry), corresponding to rotation angles of 72 degrees (360/5) and 60 degrees (360/6), respectively. If a flower has pentamerous symmetry, rotating it by multiples of 72 degrees (72, 144, 216, 288, 360) would show the flower looking the same each time. Similarly, for a flower with hexamerous symmetry, angles of rotation would be multiples of 60 degrees (60, 120, 180, 240, 300, 360). Another form of symmetry mentioned is bilateral symmetry, where only a 180-degree rotation would result in the flower appearing the same.