If the sum of interior angles of a polygon is 1620°. Then number of sides of the polygon is :

Question

Accepted Answer

To determine the number of sides of a polygon given that the sum of its interior angles is 1620°, 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 1620°, we can set up the equation:

$$ (n - 2) \times 180° = 1620° $$

Now, solve for $ n $:

1. Divide both sides by 180°:

$$ n - 2 = \frac{1620°}{180°} $$

$$ n - 2 = 9 $$

2. Add 2 to both sides to solve for $ n $:

$$ n = 9 + 2 $$

$$ n = 11 $$

Therefore, the polygon has 11 sides, which corresponds to Option 3.

### Explanation of Incorrect Options:

- **Option 1 (9 sides):** If the polygon had 9 sides, the sum of its interior angles would be:

$$ (9 - 2) \times 180° = 7 \times 180° = 1260° $$

This does not match the given sum of 1620°, so Option 1 is incorrect.

- **Option 2 (10 sides):** If the polygon had 10 sides, the sum of its interior angles would be:

$$ (10 - 2) \times 180° = 8 \times 180° = 1440° $$

This also does not match the given sum of 1620°, so Option 2 is incorrect.

- **Option 4 (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 exceeds the given sum of 1620°, so Option 4 is incorrect.

In conclusion, the only option that satisfies the condition of the sum of interior angles being 1620° is Option 3, which corresponds to a polygon with 11 sides.