Question

Deanna is investigating transformations that carry a regular polygon onto itself. She claims that for a regular polygon of k sides, the minimum angle of rotation about its center that carries it onto itself is equal to the measure of each interior angle of the polygon. For what value of k would Deanna's claim be true?

Answer 1

The value of k that would make Deanna's claim to be true is k = 4

Explanation:

The given transformation that Deanna has a claim for = Rotation

Deanna's claim. the minimum rotation of a polygon about its center that carries the polygon onto itself = The interior angle of the polygon

We note that the rotation of a regular polygon about its center that carries the polygon onto itself = The exterior angle of the polygon

Therefore, given that for a polygon with more than 5 sides, the exterior angle of the polygon < The interior angle of the polygon, Deana statement can be said to be true for the case of a square

Here;

The exterior angle of the polygon = The interior angle of the polygon 90

The value of k which is the number of sides of the polygon, for a square = 4

Therefore, the value of k that would make Deanna's claim to be true is k = 4.