Question

find the measure of an interior angle of a regular dodecagon (12 - sided polygon). hint: sum=(n - 2)180

Explanation:

Step1: Find sum of interior angles

For a polygon with $n$ sides, the sum of interior - angles formula is $S=(n - 2)\times180^{\circ}$. Here, $n = 12$, so $S=(12 - 2)\times180^{\circ}=10\times180^{\circ}=1800^{\circ}$.

Step2: Calculate measure of one interior angle

Since the dodecagon is regular, all interior angles are equal. Let the measure of one interior angle be $x$. Then $x=\frac{S}{n}$. Substituting $S = 1800^{\circ}$ and $n = 12$, we get $x=\frac{1800^{\circ}}{12}=150^{\circ}$.

Answer:

$150$