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

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Multiple Choice

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

The sum of interior angles in a polygon can be found by triangulating the shape and using that each triangle has 180 degrees. When you draw diagonals from one vertex to all nonadjacent vertices, a pentagon is divided into three triangles. Since each triangle contributes 180 degrees, the total is 3 × 180 = 540 degrees. Why the other numbers don’t fit a pentagon: 360 degrees would come from a four-sided figure, 720 degrees from a six-sided figure, and 900 degrees from a seven-sided figure.

The sum of interior angles in a polygon can be found by triangulating the shape and using that each triangle has 180 degrees. When you draw diagonals from one vertex to all nonadjacent vertices, a pentagon is divided into three triangles. Since each triangle contributes 180 degrees, the total is 3 × 180 = 540 degrees.

Why the other numbers don’t fit a pentagon: 360 degrees would come from a four-sided figure, 720 degrees from a six-sided figure, and 900 degrees from a seven-sided figure.

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