The center corner of a regular polygon can’t be obtuse?

The sum of all the central angles of a regular polygon is 360 ° and they are equal, i.e. the center angle is 360 ° / N, where N is the number of all corners of the polygon.

An obtuse angle is an angle that is greater than a 90 ° right angle.

It is easy to make sure that at N≥4 the value is 360 ° / N ≤ 90 °, which means that the angle cannot be obtuse.

But in the case of a regular triangle, when N = 3, the central angle is 120 ° and is obtuse.

Answer: It can only be for a regular triangle.