Question

Which rotation about its center will carry a regular decagon onto itself

Answer 1

Answer:

The answer is any multiple of 36.

Step-by-step explanation:

A decagon has 10 sides, and it has 10 exterior angles of 36° as can be seen in the picture.

Therefore, by rotating the decagon about its center by multiples of 36° will carry a regular decagon onto itself.

Any multiple of 36 could be: 36, 72, 108, 144, 180, 216, 252, 288, etc...

Answer 2

A decagon has 10 sides so every 36 degrees, you would encounter another side.
So, the answer is a 36 degree rotation.