In case (a) and (b) aren't immediately obvious: The net change in direction around a triangle, quadrilateral, or any simple closed curve is a full rotation, i.

In case (a) and (b) aren't immediately obvious: The net change in direction around a triangle, quadrilateral, or any simple closed curve is a full rotation, i.e., 2π. The sum of the interior angle and the signed change in direction around a vertex of a polygon is π (consider the case of a "vertex" with interior angle π). So for a polygon with interior angles θ₁, θ₂, …, θₙ, 2π = (π - θ₁) + (π - θ₂) + ⋯ + (π - θₙ), therefore θ₁ + θ₂ + ⋯ + θₙ = nπ - 2π = (n-2)π.