In a regular polygon
- All sides are equal
- All angles are equal
Let
∠ A = ∠ B = ∠ C = ∠ D = ∠ E = ∠ F = x
We know that
Sum of angles of a regular hexagon = (n – 2) × 180°
Putting n = 6
= (6 – 2) × 180°
= 4 × 180°
= 720°
Now,
Sum of angles of a regular hexagon= 720°
∠ A + ∠ B + ∠ C + ∠ D + ∠ E + ∠ F = 720°
x + x + x + x + x + x = 720°
6x = 720°
x = (720°)/6
x = 120°
Thus,
Interior Angle of a Regular Hexagon = 120°
In general
Interior Angle of a Polygon × Number of sides = Sum of angles
Interior Angle of a Regular Polygon × n = (n – 2) × 180°
Interior Angle of a Regular Polygon = ((n - 2))/n × 180°