Note 2( Different method to find out the interior angles in a polygon)

 

Sum of Interior Angles in a Polygon

The interior angles of a polygon are those angles that lie inside the polygon. Observe the interior angles A, B, and C in the following triangle. The interior angles in a regular polygon are always equal to each other. Therefore, to find the sum of the interior angles of a polygon, we use the formula: Sum of interior angles = (n − 2) × 180° where 'n' = the number of sides of a polygon.

  Sum of Interior Angles of a polygon

Another way to calculate the sum of the interior angles is by checking the number of triangles formed inside the polygon with the help of the diagonals. Since the interior angles of a triangle sum up to 180°, the sum of the interior angles of any polygon can be calculated by multiplying 180° with the number of triangles formed inside the polygon. For example, a quadrilateral can be divided into two triangles using the diagonals, therefore, the sum of the interior angles of a quadrilateral is 2 × 180° = 360°. Similarly, a pentagon can be divided into 3 triangles, so, the pentagon's interior angles will sum up to 3 × 180° = 540°

Example:

What is the Sum of the Interior Angles in a Hexagon?

Solution: 

A hexagon has 6 sides, therefore, n = 6

The sum of interior angles of a regular polygon, S = (n − 2) × 180

S = (6-2) × 180°

⇒ S = 4 × 180

⇒ S=720°

Therefore, the sum of interior angles of a hexagon is 720°.