Polygons

The number of diagonals in a regular polygon is $2.5$-times bigger than the number of the sides of this polygon. In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find the central angle of the polygon.

Consider a rectangle $ABCD$ of a special ratio between the length and the width: if $E$, $F$, $G$ and $H$ denote the midpoints of the sides $AB$, $BC$, $CD$ and $DA$, respectively, then the measure of the angle $AEH$ is ${25}^{\circ }$. Find the measure of the angle $EFG$.

Consider a rectangle $ABCD$ and a point $S$ which is the intersection of diagonals. The measure of the angle $BAS$ is ${60}^{\circ }$. Find the measure of the angle $BSC$.

Consider a regular polygon with the central angle of ${20}^{\circ }$. In the figure the cut of a regular polygon with unspecified number of vertices is shown. The red angle is the central angle of the polygon. Find the number of vertices of this polygon.