# What is the measure of one interior angle in a 24-gon?

May 3, 2018

${3960}^{\circ}$

#### Explanation:

Given: $24$-gon

The interior angles are based on the number of sides:

$\underline{n \text{ number of triangles interior angles}}$
$3 \text{ "1" } {180}^{\circ}$
$4 \text{ "2" } 2 \cdot {180}^{\circ} = {360}^{\circ}$
$5 \text{ "3" } 3 \cdot {180}^{\circ} = {540}^{\circ}$
$6 \text{ "4" } 4 \cdot {180}^{\circ} = {720}^{\circ}$
...

$24 \text{ "22" } 22 \cdot {180}^{\circ} = {3960}^{\circ}$

The formula: $\left(n - 2\right) \cdot {180}^{\circ}$, where $n$ = number of sides