Answer to Question #223285 in Geometry for Basy

Question

A polygon has (2n+5) sides. The sum of the interior angles of the polygon is ?

Answer 1

The sum of the interior angles of a convex polygon is equal to $(m - 2)\cdot180\degree$ where $m$ is the number of sides.

Given $m=2n+5.$

Then the sum of the interior angles of a convex polygon is equal to

$$(m - 2)\cdot180\degree=(2n+5 - 2)\cdot180\degree$$

$$=(2n+3)\cdot180\degree$$