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

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

• A. 540 degrees
• B. 360 degrees
• C. 720 degrees
• D. 180 degrees

Answer: (A)

To determine the sum of the interior angles in a pentagon, we can use the formula for the sum of the interior angles of a polygon, which is given by the equation: Sum of interior angles = (n - 2) × 180 degrees, where n is the number of sides of the polygon. For a pentagon, which has five sides, we can substitute n with 5: Sum of interior angles = (5 - 2) × 180 degrees = 3 × 180 degrees = 540 degrees. This calculation shows that the sum of the interior angles in a pentagon is 540 degrees, making it the correct answer. The other options represent sums for different shapes. For example, a triangle has a total of 180 degrees, which is why one of the options is 180 degrees. A quadrilateral, with four sides, has a sum of interior angles of 360 degrees, which corresponds to another option. Lastly, a hexagon has six sides and a sum of 720 degrees. Therefore, the correct answer highlights the specific characteristics and calculations relevant to pentagons.

To determine the sum of the interior angles in a pentagon, we can use the formula for the sum of the interior angles of a polygon, which is given by the equation:

Sum of interior angles = (n - 2) × 180 degrees,

where n is the number of sides of the polygon. For a pentagon, which has five sides, we can substitute n with 5:

Sum of interior angles = (5 - 2) × 180 degrees

= 3 × 180 degrees

= 540 degrees.

This calculation shows that the sum of the interior angles in a pentagon is 540 degrees, making it the correct answer.

The other options represent sums for different shapes. For example, a triangle has a total of 180 degrees, which is why one of the options is 180 degrees. A quadrilateral, with four sides, has a sum of interior angles of 360 degrees, which corresponds to another option. Lastly, a hexagon has six sides and a sum of 720 degrees. Therefore, the correct answer highlights the specific characteristics and calculations relevant to pentagons.