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Select the correct answer:

A regular polygon has an exterior angle measuring [tex]$30^{\circ}$[/tex]. How many sides does the polygon have?

A. 10
B. 8
C. 14
D. 12


Sagot :

To determine the number of sides of a regular polygon given that each exterior angle measures \(30^\circ\), we can use the following concept of polygon exterior angles:

1. The sum of exterior angles of any polygon is always \(360^\circ\).
2. In a regular polygon (all sides and all angles are equal), each exterior angle can be found by dividing \(360^\circ\) by the number of sides \(n\).

Given:
- Each exterior angle is \(30^\circ\).

Step-by-Step Solution:
1. Use the formula for the exterior angle of a regular polygon:
[tex]\[ \text{Exterior angle} = \frac{360^\circ}{n} \][/tex]

2. Substitute the given exterior angle \(30^\circ\) into the formula:
[tex]\[ 30^\circ = \frac{360^\circ}{n} \][/tex]

3. Solve for \(n\) (number of sides):
[tex]\[ n = \frac{360^\circ}{30^\circ} \][/tex]

4. Calculate the value:
[tex]\[ n = 12 \][/tex]

So, the regular polygon with each exterior angle measuring \(30^\circ\) has \(12\) sides.

Thus, the correct answer is:
D. 12