Question

Find the sum of the interior angles of a 25-sided polygon

Answer 1

4140°

Explanation:

The exterior angles of a polygon add up to 360°. So the exterior angle of this polygon is 360 ÷ 25 = 14.4°

The interior angle of the polygon is 180 - 14.4 = 165.6°

The sum of the interior angles is 165.6 × 25 = 4140°

Answer 2

4140°

Explanation:

To find sum of interior angles of a polygon with
`n` sides we apply the following formula:

`S=(n-2) 180`

where
`S` represents the sum of interior angles of the polygon and
`n` represents number of sides of the polygon.

Thus, for a 25-sided polygon the sum of interior angles can be calculated by plugging in
`n=25` in the formula.

`S=(25-2) 180`

`S=(23) 180`

∴
`S=4140\°` (Answer)