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°

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*
*
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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°

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Interior Angle of a
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Regular Polygon
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=
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((n - 2))/n
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× 180°
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