Each interior angle of a regular polygon measures 120 degree and write an equation to find the number of sides n in this polygon and solve?

Answer 1

Two approaches:

Option A: Interior angle = x => exterior angle = 180 - x. Sum of n exterior angles = 360.

Thus: Number of sides = 360/(180 - x)

Option B: Sum of n interior angles is (n-2)*180 degrees so each one is (n-2)/n*180

which can be shown to simplify to n = 360/(180-x)

Answer 2

Let the sides be x:-

180-120 = 360/x => 60 = 360/x => 60x = 360 => x = 6

Therefore it is a regular 6 sided hexagon