If a polygon has six sides, what is the sum of its interior angles?

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Multiple Choice

If a polygon has six sides, what is the sum of its interior angles?

The sum of interior angles in any polygon with n sides is (n − 2) × 180 degrees. This comes from dividing the polygon into triangles: from one vertex, draw diagonals to all nonadjacent vertices, which creates n − 2 triangles. Each triangle contributes 180 degrees, so the total is (n − 2) × 180. For a polygon with six sides, n = 6, so it can be split into 4 triangles. The total interior angle sum is 4 × 180 = 720 degrees. (For context: a five-sided polygon would have (5 − 2) × 180 = 540 degrees, a seven-sided polygon would have 900 degrees, and an eight-sided polygon would have 1080 degrees.)

The sum of interior angles in any polygon with n sides is (n − 2) × 180 degrees. This comes from dividing the polygon into triangles: from one vertex, draw diagonals to all nonadjacent vertices, which creates n − 2 triangles. Each triangle contributes 180 degrees, so the total is (n − 2) × 180.

For a polygon with six sides, n = 6, so it can be split into 4 triangles. The total interior angle sum is 4 × 180 = 720 degrees.

(For context: a five-sided polygon would have (5 − 2) × 180 = 540 degrees, a seven-sided polygon would have 900 degrees, and an eight-sided polygon would have 1080 degrees.)

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