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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°

Interior Angles of Regular Polygons - Part 2

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°

 

 

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.