Question

1. hexagon

symmetric?____
number of symmetries____
degree of each symmetry____

Explanation:

Step1: Define symmetry

A regular hexagon has both rotational and reflectional symmetries.

Step2: Count symmetries

For a regular hexagon, there are 6 reflection - lines (3 through opposite vertices and 3 through mid - points of opposite sides) and 6 rotational symmetries (rotation by 0°, 60°, 120°, 180°, 240°, 300°). So in total, there are 12 symmetries.

Step3: Determine degrees of rotation symmetries

The degrees of rotational symmetries are 0°, 60°, 120°, 180°, 240°, 300°. For reflection symmetries, we can consider them as having a "degree" of 1 (a single flip). But if we focus on rotation, the non - zero rotation degrees are 60°, 120°, 180°, 240°, 300°.

Answer:

Symmetric? Yes
Number of symmetries: 12
Degree of each symmetry: For rotations: 0°, 60°, 120°, 180°, 240°, 300°; for reflections, conceptually 1 (in terms of flip)