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CBSE Class 8 Answered

Can you show the derivation of "the sum of the interior angles of a regular polygon with n sides is always (n-2)x180"?
Asked by biswajitpatel88 | 10 May, 2024, 01:54: PM
answered-by-expert Expert Answer

Consider the following polygon.

Through a single vertex of a polygon, draw all possible diagonals.

Here, the number of sides of a polygon = 5 = n

And, the number of triangles formed = 3 = n - 2

That is, if the number of sides of a polygon is n, the number of triangles formed will be (n - 2).

The sum of the angles of a triangle = 180 degrees

Then, the sum of the angles of (n - 2) triangles = (n - 2) x 180 degrees

Hence, the sum of interior angles of a polygon with n sides = (n - 2) x 180 degrees

 

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