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?

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

Step-by-step 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.

3/6   and 9/18

step-by-step explanation:

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.