What is the formula to calculate the number of sides in a polygon if given the sum of interior angles?

What is the formula to calculate the number of sides in a polygon if given the sum of interior angles?

• A. n = (sum / 180) + 2
• B. n = (sum / 180) - 2
• C. n = (sum + 360) / 180
• D. n = (sum + 2) / 180

Answer: (A)

The formula for calculating the number of sides in a polygon based on the sum of its interior angles is derived from the relationship between the number of sides (n) and the sum of interior angles. The sum of the interior angles of a polygon with n sides can be calculated using the formula: Sum = (n - 2) * 180. To isolate n and formulate it in terms of the sum, you rearrange this equation. Starting with: Sum = (n - 2) * 180 you can divide both sides by 180: Sum / 180 = n - 2. By adding 2 to both sides, you get: n = (Sum / 180) + 2. This establishes that if you know the sum of the interior angles of a polygon, you can determine the number of sides by this formula. Therefore, the correct answer effectively captures this relationship, confirming that the number of sides is directly calculated from the sum of the interior angles.

The formula for calculating the number of sides in a polygon based on the sum of its interior angles is derived from the relationship between the number of sides (n) and the sum of interior angles. The sum of the interior angles of a polygon with n sides can be calculated using the formula:

Sum = (n - 2) * 180.

To isolate n and formulate it in terms of the sum, you rearrange this equation. Starting with:

Sum = (n - 2) * 180

you can divide both sides by 180:

Sum / 180 = n - 2.

By adding 2 to both sides, you get:

n = (Sum / 180) + 2.

This establishes that if you know the sum of the interior angles of a polygon, you can determine the number of sides by this formula. Therefore, the correct answer effectively captures this relationship, confirming that the number of sides is directly calculated from the sum of the interior angles.