# What is the sum of the interior angles of a hendecagon?

Dec 19, 2015

Sum of interior angles of a hendecagon $= {1620}^{\circ}$

#### Explanation:

The real issue here is knowing that a "hendecagon" is an $11$ sided (and angled) polygon.

The formula for the sum of the interior angles of an $n$-gon is
$\textcolor{w h i t e}{\text{XXX")180^@xx(n-2)color(white)("XXXXX}}$provided $n \ge 3$

An $11$-gon (hendecagon) can be divided into $9$ triangles by connecting vertices; each triangle has an interior angle sum of ${180}^{\circ}$

Sum of interior angles of hendecagon $= {180}^{\circ} \times 9 = {1620}^{\circ}$