The so-called "dense shop" can just spell out a complete 360.
Exceeding or not enough is unacceptable.
Then just find out the degree of the internal angle of the regular triangle, the regular quadrilateral ... a regular decagon.
Regular triangle: 60, right.
Regular quadrilateral: 90, right.
Regular Pentagon: 108, no.
Regular hexagon: 120, yes.
Regular heptagon: 900/7, no.
Regular octagon: 135, no.
True nonagon: 140, No.
Regular decagon: 144, no.