To calculate the degrees in a pentagon, what formula would you use?

To calculate the degrees in a pentagon, what formula would you use?

• A. 3 x 180
• B. (5 - 2) x 180
• C. 5 x 180
• D. 5 - 2

Answer: (B)

In a pentagon, the formula to calculate the total sum of the interior angles is based on the number of sides (n) the polygon has. The formula is (n - 2) x 180 degrees. Since a pentagon has 5 sides, substituting 5 into the formula gives us (5 - 2) x 180, which simplifies to 3 x 180. Thus, the total sum of the interior angles for a pentagon is 540 degrees. This formula works because it calculates how many triangles can be formed within the polygon; each triangle has a total of 180 degrees. For a pentagon, you can create three triangles (hence, 5 sides - 2 equals 3), leading to the total angle sum. Using this reasoning, it is clear why the selected option is the correct choice for finding the total degrees in a pentagon.

In a pentagon, the formula to calculate the total sum of the interior angles is based on the number of sides (n) the polygon has. The formula is (n - 2) x 180 degrees. Since a pentagon has 5 sides, substituting 5 into the formula gives us (5 - 2) x 180, which simplifies to 3 x 180. Thus, the total sum of the interior angles for a pentagon is 540 degrees.

This formula works because it calculates how many triangles can be formed within the polygon; each triangle has a total of 180 degrees. For a pentagon, you can create three triangles (hence, 5 sides - 2 equals 3), leading to the total angle sum.

Using this reasoning, it is clear why the selected option is the correct choice for finding the total degrees in a pentagon.