Skill: Determine the sum of interior angles of a polygon

For a simple polygon with $n$ sides, the sum of its interior angles is

$$(n-2)\times 180^\circ.$$

This works because the polygon can be divided into $n-2$ triangles. Each triangle has an angle sum of $180^\circ$.

Example: Find the sum of the interior angles of an octagon.

1. An octagon has $8$ sides, so $n=8$.

2. Substitute $8$ into the formula:

$$(8-2)\times 180^\circ$$

3. Simplify:

$$6\times 180^\circ=1080^\circ$$

Therefore, the sum of the interior angles of the octagon is

$$\boxed{1080^\circ}.$$

The answer depends only on the number of sides, not on the polygon’s size, shape, or whether it is regular.