Question

Tessa claims that for a regular polygon of n sides, the smallest angle for a rotation about the polygon's center that carries the polygon onto itself is 30°. What value of n (the number of sides) that will make Tessa's claim true?

Answer 1

Tessa's claim is true for a dodecagon, which is a regular polygon with 12 sides. To determine this, we solve 360° divided by the number of sides (n) equals 30°, resulting in n being equal to 12.

Step-by-step explanation:

The student's question asks for the value of n that would make a regular polygon have the smallest angle of rotation about its center, which maps the polygon onto itself, be 30°. For a regular polygon, the smallest angle of rotation is 360° divided by the number of sides, n. Thus, we need to solve the equation 360° / n = 30°.

Dividing both sides by 30° gives us n = 360°/30°, which simplifies to n = 12. Therefore, Tessa's claim is true for a regular polygon with 12 sides, which is known as a dodecagon.