Revision: Geometry >> Polygons Maths ICSE ICSE Class 6 CISCE

A polygon is any closed, flat shape that is formed by straight line segments (sides).

Example:

A polygon is a closed, flat figure made up of straight-line segments. A polygon is called a regular polygon if it is both:

1. Equiangular: All its interior angles are equal.

2. Equilateral: All its sides are equal in length.

Sum of interior angles of a polygon = (n – 2) × 180°

Explanation:

• A polygon with n sides can be divided into smaller triangles by drawing diagonals from one vertex.
• Each triangle has a total angle sum of 180°.
• Since the number of triangles formed inside the polygon is (n – 2).
• The total sum of all interior angles is therefore (n – 2) × 180°.

Each exterior angle = `"360°"/"n"`

Sum of interior angles = (n − 2) × 180^∘

Each interior angle = `"(n − 2) × 180° " /"n"`

Number of sides (n) of a regular polygon = `"360°"/"exterior angle "`

Relationship between interior and exterior angles = Exterior angle + Interior angle = 180°