Question

Prove that the sum of all exterior angles of any polygon is 360 degree

Answer 1

Sum of all exterior angles = n × 180° - (n -2) × 180°

= n × 180° - n × 180° + 2 × 180°

= 180°n - 180°n + 360°

= 360°

Answer 2

Question-

Prove that the sum of the exterior angles of a polygon is equal to 360 degrees.

Answer-

Consider a polygon with n number of sides or an n-gon. The sum of its exterior angles is N.

For any closed structure, formed by sides and vertex, the sum of the exterior angles is always equal to the sum of linear pairs and sum of interior angles. Therefore,

N = 180n – 180(n-2)

N = 180n – 180n + 360

N = 360