Question

What is the measure of one interior angle of a regular 12-gon?

Answer 1

the formula who gives us the measure of the interior angles in a regular polygon is
(n-2)*180, where n is the number of sides
(12-2)*180=10*180=1800 degrees
1800/12=150
one interior angle is 150 in a dodecagon

Answer 2

Find the value of the exterior angle of a 12 sided side of polygon first.
all of the exterior angles of a regular n gon add up to 360. So the general formula for one of the exterior angles is 360 / n for 1 exterior angle.
In your case 1 exterior angle = 360 / 12 = 30o

I've made such a fuss about the exterior angle because 1 exterior angle + 1 interior angle = 180o In other words the two angles are supplementary.
30 + interior angle = 180
interior angle = 180 - 30
interior angle = 150 <<<< answer