Sum of the interior angles of a regular heptagon is :

Question

Accepted Answer

The sum of the interior angles of a regular heptagon is calculated using the formula for the sum of the interior angles of a polygon, which is:

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

where $ n $ is the number of sides of the polygon. For a heptagon, $ n = 7 $.

Substituting the value of $ n $ into the formula:

$$
\text{Sum of interior angles} = (7 - 2) \times 180^\circ = 5 \times 180^\circ = 900^\circ
$$

Therefore, the sum of the interior angles of a regular heptagon is indeed 900°, which corresponds to Option 4.

Now, let's explain why the other options are incorrect:

1. **Option 1: 1200°** - This value is incorrect because it does not match the calculated sum of 900° for a heptagon. The calculation for 1200° would imply a different polygon with more sides.

2. **Option 2: 1050°** - This value is also incorrect. A sum of 1050° would correspond to a polygon with more than 7 sides. Specifically, it would be the sum of the interior angles of an octagon, not a heptagon.

3. **Option 3: 720°** - This value is incorrect as well. A sum of 720° corresponds to a hexagon, which has 6 sides, not a heptagon.

In conclusion, the correct sum of the interior angles of a regular heptagon is 900°, which is why Option 4 is the correct answer.