What is the sum of the interior angles of a pentagon?

What is the sum of the interior angles of a pentagon?

• A. 360 degrees
• B. 540 degrees
• C. 720 degrees
• D. 900 degrees

Answer: (B)

To determine the sum of the interior angles of a pentagon, one can use the formula for calculating the sum of the interior angles of any polygon. This formula states that the sum of the interior angles in a polygon can be found using the equation: Sum of angles = (n - 2) × 180 degrees where "n" represents the number of sides in the polygon. For a pentagon, which has 5 sides, we substitute n with 5: Sum of angles = (5 - 2) × 180 degrees Sum of angles = 3 × 180 degrees Sum of angles = 540 degrees Thus, the sum of the interior angles of a pentagon is 540 degrees. This value results from the fact that as the number of sides increases, the potential for internal angles to create a more complex shape increases, leading to a greater total sum. The derived total of 540 degrees is significant, as it reflects the relationship between the sides of a polygon and the interior angles formed.

To determine the sum of the interior angles of a pentagon, one can use the formula for calculating the sum of the interior angles of any polygon. This formula states that the sum of the interior angles in a polygon can be found using the equation:

Sum of angles = (n - 2) × 180 degrees

where "n" represents the number of sides in the polygon. For a pentagon, which has 5 sides, we substitute n with 5:

Sum of angles = (5 - 2) × 180 degrees

Sum of angles = 3 × 180 degrees

Sum of angles = 540 degrees

Thus, the sum of the interior angles of a pentagon is 540 degrees. This value results from the fact that as the number of sides increases, the potential for internal angles to create a more complex shape increases, leading to a greater total sum. The derived total of 540 degrees is significant, as it reflects the relationship between the sides of a polygon and the interior angles formed.