The sum of interior angles of a hexagon (n=6) is (n-2)×180 degrees. Find the sum.

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Multiple Choice

The sum of interior angles of a hexagon (n=6) is (n-2)×180 degrees. Find the sum.

Explanation:
The sum of interior angles for any polygon can be found by triangulating it: a polygon with n sides can be divided into (n−2) triangles, and each triangle contributes 180 degrees. For a hexagon, n is 6, so you can split it into 4 triangles. Therefore, the total is 4 × 180 = 720 degrees. This matches the hexagon’s interior angle sum. The other numbers correspond to polygons with different numbers of sides (for example, a pentagon gives 540, a heptagon gives 900), so they don’t fit this shape.

The sum of interior angles for any polygon can be found by triangulating it: a polygon with n sides can be divided into (n−2) triangles, and each triangle contributes 180 degrees. For a hexagon, n is 6, so you can split it into 4 triangles. Therefore, the total is 4 × 180 = 720 degrees. This matches the hexagon’s interior angle sum. The other numbers correspond to polygons with different numbers of sides (for example, a pentagon gives 540, a heptagon gives 900), so they don’t fit this shape.

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