To determine the number of sides of a regular polygon based on its exterior angle, we'll use a fundamental property of polygons.
The exterior angle of a regular polygon is given by:
[tex]\[ \text{Exterior Angle} = \frac{360^\circ}{\text{Number of Sides}} \][/tex]
Let's denote the number of sides of the polygon as [tex]\( n \)[/tex].
Given that the exterior angle is [tex]\( 30^\circ \)[/tex], we can set up the equation:
[tex]\[ 30^\circ = \frac{360^\circ}{n} \][/tex]
To find [tex]\( n \)[/tex], we simply solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{360^\circ}{30^\circ} \][/tex]
[tex]\[ n = 12 \][/tex]
Therefore, the number of sides of the polygon is 12.
So, the correct answer is:
D. 12
