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

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

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

Answer: (B)

The sum of the interior angles of a polygon can be determined using the formula: \[ \text{Sum of interior angles} = (n - 2) \times 180 \] where \( n \) represents the number of sides in the polygon. For a pentagon, which has five sides, we can substitute \( n = 5 \) into the formula: \[ \text{Sum of interior angles} = (5 - 2) \times 180 = 3 \times 180 = 540 \text{ degrees} \] This means that the total measure of all the interior angles in a pentagon is 540 degrees. Thus, the correct answer is indeed 540 degrees, as it accurately reflects the mathematical principles for calculating the interior angles of a pentagon.

The sum of the interior angles of a polygon can be determined using the formula:

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

where ( n ) represents the number of sides in the polygon. For a pentagon, which has five sides, we can substitute ( n = 5 ) into the formula:

[ \text{Sum of interior angles} = (5 - 2) \times 180 = 3 \times 180 = 540 \text{ degrees} ]

This means that the total measure of all the interior angles in a pentagon is 540 degrees. Thus, the correct answer is indeed 540 degrees, as it accurately reflects the mathematical principles for calculating the interior angles of a pentagon.