Which formula gives the sum of interior angles of an n-sided polygon?

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Multiple Choice

Which formula gives the sum of interior angles of an n-sided polygon?

Think about dividing the polygon into triangles. An n-sided polygon can be partitioned into exactly n−2 non-overlapping triangles. Each triangle has interior angles that sum to 180 degrees, so the whole polygon’s interior angles total (n−2)×180 degrees. This matches familiar cases: a triangle gives 180 degrees, a quadrilateral gives 360 degrees, a pentagon gives 540 degrees, and so on. The other formulas don’t fit these checks—n×180 would give 540 for a triangle (too large), (n−1)×180 would give 360 for a triangle (also too large), and n×90 would give 270 for a triangle (incorrect). The correct expression is (n−2)×180 degrees.

Think about dividing the polygon into triangles. An n-sided polygon can be partitioned into exactly n−2 non-overlapping triangles. Each triangle has interior angles that sum to 180 degrees, so the whole polygon’s interior angles total (n−2)×180 degrees. This matches familiar cases: a triangle gives 180 degrees, a quadrilateral gives 360 degrees, a pentagon gives 540 degrees, and so on. The other formulas don’t fit these checks—n×180 would give 540 for a triangle (too large), (n−1)×180 would give 360 for a triangle (also too large), and n×90 would give 270 for a triangle (incorrect). The correct expression is (n−2)×180 degrees.

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