Question

How to prove that in a n sided polygon sum of all angles is 180°(n-2) ?

Answer 1

just take a n-sided polygon , from one vertex join all vertices except the adjacent ones(as they are already joined)

now you will see that you are getting (n-2) triangles everytime and so sum of all angles = (n-2)*180

Eg. in a quad we can draw 2 traingles like explained above,so sum of angles = (4-2) * 180 = 360

in a pentagon choose a vertex and then join other vertices , you will get 3 triangles so sum is 3*180 =540

Answer 2

take a triangle it has the sum of angles 180

in a square the sum of angles is 360 = 180+180

⇒square has sides n sides and sum of angles is (n-2)180

it also applies for other polygon

this formula should be understood not derived

hope helped