Question

How do you find the sum of the interior angle measures in 24-gon?

Answer 1

`S = (n - 2)180^@` For 24 sides: `S = 3960^@`

Explanation:

Here is a reference Interior angles of a polygon

The general formula for the sum, S, of the measure of the interior angles of a polygon with n sides is:

`S = (n - 2)180^@`

Answer 2

The sum of the interior angles of a `24`-gon is 3960.

Explanation:

The formula for the sum of the interior angles of a polygon is `(n-2)*180`, where `n` is the number of sides.

For a `24`-gon, `n=24`.

`(24-2)* 180 = 3960`.

Another method is to use exterior angles. An `n`-gon has `n` exterior angles.

An exterior angles measures `360/n`.

An interior angle equals `180` minus the exterior angle.

A `24`-gon has `24` exterior angles.

Each exterior angle measures `360/24=15`.

The interior angle measures `180-15=165`.

The sum of the `24` interior angles is then `24*165=3960`.