Question

The sum of the interior angles of an n-gon is _____(n - 2).

360°
180°
270°
540°

Answer 1

the sum of the interior angles is 180°

Answer 2

The sum of the interior angles of an n-sided polygon can be calculated using formula

`\Sigma =(n-2)\cdot 180^(\circ).`

It is easy to verify:

1. If n=3 (the smallest possible number of sides for polygon), then the polygon is triangle and the sum of the measures of interior angles of triangle is always 180° .

2. If n>3, draw (n-3) diagonals from one vertex. This diagonals partition the polygon into (n-2) triangles. Thus, the sum of the interior angles of an n-sided polygon is equal to the sum of the measures of interior angles of (n-2) triangles that is

`\Sigma =(n-2)\cdot 180^(\circ).`

Answer: correct choice is B