Answer :
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
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
