Yup.. I got it, in shortest way u can say that(n-2)180 is the formula to calculate sum of interior angles rightStep1- Divide the polygon into triangles using full diagonalsStep 2- Interior angles of a triangle add up to 180° (anglesum prop. of triangle).... Is it correct??

Understanding Polygon Interior Angles
The sum of the interior angles of a polygon can be derived using basic geometric principles. Here’s a detailed explanation:
Definition of a Polygon
- A polygon is a closed figure formed by three or more sides.
- Each polygon has vertices (corners) where two sides meet.
Triangles as Building Blocks
- A polygon can be divided into triangles.
- The simplest polygon, a triangle, has an angle sum of 180°.
Dividing the Polygon
- For a polygon with 'n' sides:
- Draw diagonals from one vertex to all non-adjacent vertices.
- This divides the polygon into (n-2) triangles.
Calculating the Angle Sum
- Each triangle contributes 180° to the sum of interior angles.
- Therefore, for (n-2) triangles, the total interior angle sum is:
- (n-2) × 180°.
Final Formula
- Thus, the formula for the sum of the interior angles of an n-sided polygon is:
- (n-2) × 180°.
Example
- For a quadrilateral (n=4):
- Sum of interior angles = (4-2) × 180° = 2 × 180° = 360°.
In summary, the sum of the interior angles of a polygon with 'n' sides is derived from the number of triangles formed, leading to the formula (n-2) × 180°. This principle is fundamental in understanding polygon geometry.