The number of sides that the polygon with each exterior angle measuring 30° has is 12.
A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
The sum of all the exterior angles of a regular polygon is always equal to 360°. Therefore, the measure of an exterior angle for a regular polygon is given as,
[tex]\theta = \dfrac{360^o}{n}[/tex]
where n is the number of sides.
Given that the measure of the exterior angle is 30°. Therefore, the number of sides will be,
[tex]\theta = \dfrac{360^o}{n}\\\\ 30^o = \dfrac{360^o}{n}\\[/tex]
n = 12
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