All regular polygons (n-corners) have sides of equal length and interior angles of equal size and are therefore convex - https://domyhomework.club/ . The sum of angles in the n-corner is (n - 2) - 180°. In the regular n-corner, this angle sum is evenly distributed over all n interior angles of the n-corner.
For the size of each interior angle in a regular n-corner holds:
Every regular n-square can have a circle inscribed in it and a circle inscribed around it. The sides of the n-corner are chords of the incircle and at the same time tangents of the circumcircle.
The incircle and the circumcircle have the same centre - pay someone to do my math homework . This centre can be constructed (as the centre of the circumcircle) for a given n-corner:
Because each side of the n-corner is a chord of the circle, its central perpendicular passes through the centre of the circle.
If you connect the centre of the circumcircle with each corner point, the n-corner is divided into n isosceles triangles that are congruent to each other - https://domyhomework.club/statistic-homework/ . The following applies to the angles of the triangles:
α=360°n(the nth part of the solid angle) and β=180°-α2=90°-180°n
Thus the interior angle of the n-corner is 2 - β. For the radius r of the incircle, r⋅cos α2=r⋅cos 180°n, where r is the radius of the circumcircle.