Question

Why sum of interior angles is 540

Answer 1

This pentagon has been divided into three triangles, so the interior angles add up to 3 × 180 = 540°. In the same way, a hexagon can be divided into 4 triangles, a 7-sided polygon into 5 triangles etc. ... Remember that the formula for the sum of interior angles is (n - 2) × 180.

Answer 2

Imagine walking around the perimeter of the pentagon. No matter how irregular it is, when you get back to your starting point and are facing the same way that you were at the start you will have turned through 360°. Let's say that the exterior angles you turned through were a, b, c, d and e. 
a + b + c + d + e = 360 
The related interior angles are 180-a, 180-b, 180-c, 180-d and 180-e because each pair of interior and exterior angles add up to 180°. 
The sum of the interior angles is (180-a) + (180-b) + (180-c) + (180-d) + (180-e) 
That equals 900-(a+b+c+d+e) = 900 - 360 = 540.