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

Dec 10, 2016

$S = \left(n - 2\right) {180}^{\circ}$ For 24 sides: $S = {3960}^{\circ}$

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:

$S = \left(n - 2\right) {180}^{\circ}$

Dec 10, 2016

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 $\left(n - 2\right) \cdot 180$, where $n$ is the number of sides.

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

$\left(24 - 2\right) \cdot 180 = 3960$.

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

An exterior angles measures $\frac{360}{n}$.

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

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

Each exterior angle measures $\frac{360}{24} = 15$.

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

The sum of the $24$ interior angles is then $24 \cdot 165 = 3960$.