The sum of interior angle of a regular polygon is 1440°, then the number of sides is :

Question

Accepted Answer

To determine the number of sides of a regular polygon given that the sum of its interior angles is 1440°, we can use the formula for the sum of interior angles of a polygon:

$$ \text{Sum of interior angles} = (n - 2) \times 180° $$

where $ n $ is the number of sides of the polygon.

Given that the sum of the interior angles is 1440°, we can set up the equation:

$$ (n - 2) \times 180° = 1440° $$

Solving for $ n $:

1. Divide both sides by 180°:

$$ n - 2 = \frac{1440°}{180°} $$

$$ n - 2 = 8 $$

2. Add 2 to both sides:

$$ n = 8 + 2 $$

$$ n = 10 $$

Therefore, the number of sides of the polygon is 10, which corresponds to Option 2.

**Explanation for why other options are incorrect:**

- **Option 1 (8 sides):** If the polygon had 8 sides, the sum of its interior angles would be calculated as:

$$ (8 - 2) \times 180° = 6 \times 180° = 1080° $$

This does not match the given sum of 1440°, so Option 1 is incorrect.

- **Option 3 (12 sides):** If the polygon had 12 sides, the sum of its interior angles would be:

$$ (12 - 2) \times 180° = 10 \times 180° = 1800° $$

This is greater than the given sum of 1440°, so Option 3 is incorrect.

- **Option 4 (6 sides):** If the polygon had 6 sides, the sum of its interior angles would be:

$$ (6 - 2) \times 180° = 4 \times 180° = 720° $$

This is less than the given sum of 1440°, so Option 4 is incorrect.

In conclusion, the correct answer is Option 2, as it is the only option that satisfies the condition of the sum of interior angles being 1440°.