(Originais Teachy 2023) - Question Hard of Mathematics

When studying the construction of a new theme park, a group of 7th grade students from Elementary School carried out an interdisciplinary project involving Mathematics and Geometry. They designed an area that contains a large regular polygon, and one of the proposed challenges was to determine the number of sides the polygon should have so that, when divided into triangles by its sides, each of these triangles would have an internal angle that is twice its external angle. Considering that the external angle of a regular polygon is constant and is obtained by the formula 360° divided by the number of sides of the polygon, calculate how many sides the polygon will have to meet this condition. In addition, explain how the relationship between internal and external angles of regular polygons can be used to design structures that require rigid support, such as in architecture and engineering.