What is the total number of sides in a polygon if its interior angles sum to 1,080 degrees?

To determine the total number of sides in a polygon based on the sum of its interior angles, we can use the formula that relates the number of sides (n) to the sum of the interior angles. The sum of the interior angles of a polygon can be calculated with the formula:

[

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

]

In this case, we know that the sum of the interior angles is 1,080 degrees. Setting up the equation gives:

[

(n - 2) \times 180 = 1080

]

To find n, we first divide both sides of the equation by 180:

[

n - 2 = \frac{1080}{180}

]

Calculating the right side, we find:

[

n - 2 = 6

]

Next, we solve for n by adding 2 to both sides:

[

n = 6 + 2 = 8

]

Thus, a polygon with an interior angles sum of 1,080 degrees must have 8 sides, making it an octagon. This approach confirms that the answer is indeed correct, as the established