Interior Angles of Regular Polygons

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°