We can divide a polygon into some triangles. The sum of angles of total number of triangle gives us total interior angle of a polygon.

We see that,

  1. 4 sides (a, b, c, d) make 2 triangle.
  2. Then, remaining each sides make one triangle for each.

In the first case, we are losing 2 triangle according to our sides.

So we get total triangle = number of sides – 2.

And we know that, sum of angles of a triangle is 180◦.

Then total interior angle is = (number of sides – 2) * 180◦.

Finally we get,
Each interior angle = total interior angle/number of sides

As, number of sides = number of angles of a polygon.



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