Angle in a Regular Polygon

Finding the sum of the angles in a regular polygon

Solution:: The polygon refers to a figure which is closed and regular polygon means all the sides are of equal length.

3 - equal sides    ::   Equilateral triangle
4 - equal sides    ::   Square
5 - equal sides.   ::   Regular Pentagon
6 - equal sides    ::   Regular Hexagon

Sum of the angles in a triangle is 180°
                                 in a square is 360°
                                 in a pentagon is 540°
                                 in a hexagon is 720°
Sum of the angles in a n - sided polygon is (n - 2)*180°


In a regular polygon all the sides are equal which tells us all the angles are equal.

Obtaining an angle for a regular polygon :: First we will start with a triangle and we will
proceed further with the other regular polygons.

The sum of the angles in a triangle is 180°
The proof is given in SUM OF THE INTERIOR ANGLES OF A POLYGON

For a 4 - sided polygon number of triangles are 2,
          5 - sided polygon number of triangles possible are 3,
          6 - sided polygon number of triangles possible are 4

 As we sum it up for a n - sided polygon number of triangles are (n -2), n greater than or equal to 3.

Sum of the interior angles of the n - sided polygon are (n -2)*180°

Each angle in a regular polygon of n- sides is (n -2)*180°/n, n is greater than or equal to 3