Question

If the sum of the interior angles of a convex n-sided polygon can be found by using what formula?

A. 360(n - 2)

B. 180(n - 2)

C. 180n - 2

D. 360n

Answer 1

B Why?

Answer 2

If n=3 the convex n-gone is a triangle. The sum of the interior angles is 180=180(3-2)

Answer 3

If n=4 the convex n-gone is a quadrilateral. The sum of the interior angles is 360=180(4-2)

Answer 4

One can prove this in general. In a multiple choice, you do not need to do that.

Answer 5

If you take one vertex and you join it to the n-2 vertex. you get (n-2) triangles.
The sum of their angles in (n-2)180