o understand the sum of interior angles in a polygon, we should be aware of the following

The sum of all interior angles in a triangle is 180 degSum of all angles around a point is 360 degThe proof of the first property is fairly simple. Refer to the diagram below :

Next, let’s consider a pentagon. Let P be an interior point. Now, by connecting all the sides to this point we can form 5 triangles as shown in the figure. Sum of interior angles of the pentagon will be = sum of int. angles of all the triangles - sum of angles around the point.

i.e, S=5×180−360

This concept can be extended to the general case of n-sided polygon. Again, we’ll be able to form n triangles using the sides and any one unique interior point.

S=n× (sum of angles in a triangle) − (sum of angles around a point)

S=n×180−360

⇒ S=(n−2)×180

In case of pentagon, as discussed already in the above example, we’ll get S=540

Now, since each angle in a regular pentagon will be equal, we can safely conclude that all of them will have a value =5405=108 degrees

To get the value in radians, you should know the conversion factor, else you can learn it straight away.

180 degrees = π radians

⇒ 1 degree = π180 radians

⇒ 108 degrees = 108×π180 radians = 0.6π=3π5