What is the sum of interior angles of a pentagon?

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Multiple Choice

What is the sum of interior angles of a pentagon?

Explanation:
The main idea is that the interior angles of a polygon can be counted by dividing the shape into triangles. For a pentagon, draw diagonals from one vertex to the nonadjacent vertices, and you’ll split the figure into three triangles. Since each triangle has interior angles summing to 180 degrees, the pentagon’s total interior angle sum is 3 × 180 = 540 degrees. The general rule is (n − 2) × 180 for an n-gon, so for a pentagon (n = 5) you get (5 − 2) × 180 = 540 degrees. The other numbers would correspond to polygons with more sides (six sides give 720, seven sides 900), not a pentagon.

The main idea is that the interior angles of a polygon can be counted by dividing the shape into triangles. For a pentagon, draw diagonals from one vertex to the nonadjacent vertices, and you’ll split the figure into three triangles. Since each triangle has interior angles summing to 180 degrees, the pentagon’s total interior angle sum is 3 × 180 = 540 degrees. The general rule is (n − 2) × 180 for an n-gon, so for a pentagon (n = 5) you get (5 − 2) × 180 = 540 degrees. The other numbers would correspond to polygons with more sides (six sides give 720, seven sides 900), not a pentagon.

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