Question
10 of 1110 of 11 Items Question Summarize the rotations that carry a regular pentagon onto itself.(4 points) Responses A regular pentagon is a five-sided figure that has all its sides and interior angles congruent. A regular pentagon is a five-sided figure that has all its sides and interior angles congruent. A regular pentagon is a five-sided figure that has all its sides congruent but not its interior angles congruent. A regular pentagon is a five-sided figure that has all its sides congruent but not its interior angles congruent. A regular pentagon is a five-sided figure that has all its interior angles congruent but not its sides. A regular pentagon is a five-sided figure that has all its interior angles congruent but not its sides. Skip to navigation page 1 of 1
Answers
GPT-4o mini
A regular pentagon has symmetrical properties that allow it to be rotated and still coincide with itself. The rotations that carry a regular pentagon onto itself are:
1. **0 degrees (or 360 degrees)** - This is the identity rotation where the pentagon looks the same.
2. **72 degrees** - This rotation takes each vertex to the position of the next vertex.
3. **144 degrees** - This rotation moves each vertex two positions forward.
4. **216 degrees** - This rotation moves each vertex three positions forward.
5. **288 degrees** - This rotation takes each vertex four positions forward.
Thus, there are a total of 5 rotations (including the identity rotation) that carry a regular pentagon onto itself.
1. **0 degrees (or 360 degrees)** - This is the identity rotation where the pentagon looks the same.
2. **72 degrees** - This rotation takes each vertex to the position of the next vertex.
3. **144 degrees** - This rotation moves each vertex two positions forward.
4. **216 degrees** - This rotation moves each vertex three positions forward.
5. **288 degrees** - This rotation takes each vertex four positions forward.
Thus, there are a total of 5 rotations (including the identity rotation) that carry a regular pentagon onto itself.