The sum of the internal angles of a regular polygon is 1440°

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The sum of the internal angles of a regular polygon is 1440° The number of sides is

1. 8
2. 10
3. 12
4. 6

Correct Option: B

Let the number of sides of regular polygon be n.
∴ Sum of all interior angles = (2n – 4) × 90°
According to question ,
The sum of the internal angles = 1440°
⇒ (2n – 4) × 90° = 1440°
⇒ (2n – 4) = 1440° ÷ 90° = 16
⇒ 2n – 4 = 16
⇒ 2n = 16 + 4 = 20
⇒ n = 20 ÷ 2 = 10