What is the sum of the angles of the polygon?

This brochure was written based on a lecture for schoolchildren, which the author gave at the Mechanics and Mathematics Department of Moscow State University on March 25, 2017 as part of the “University Saturday” project, carried out with the support of the Moscow Department of Education. The presentation of the material significantly complements the content of the lecture and calculates It is intended for a wide range of readers interested in mathematics: high school students, junior students, high school teachers and university professors.