Answer :
To determine the number of sides in a regular polygon given the measure of an exterior angle, we use the fact that the sum of all exterior angles of any polygon is always \(360^\circ\).
Here’s a step-by-step process for solving the problem:
1. Understand the problem: We are given that the exterior angle of a regular polygon is \(30^\circ\) and we need to find the number of sides (\(n\)) of this polygon.
2. Sum of exterior angles: The sum of all exterior angles of a polygon is always \(360^\circ\).
3. Formula for exterior angle: The measure of each exterior angle of a regular polygon is given by:
[tex]\[ \text{Exterior angle} = \frac{360^\circ}{n} \][/tex]
where \(n\) is the number of sides.
4. Set up the equation: Given the exterior angle is \(30^\circ\), we substitute this into the formula:
[tex]\[ 30^\circ = \frac{360^\circ}{n} \][/tex]
5. Solve for \(n\):
[tex]\[ n = \frac{360^\circ}{30^\circ} \][/tex]
6. Calculate the number of sides:
[tex]\[ n = 12 \][/tex]
Thus, the regular polygon has 12 sides. Therefore, the correct answer is:
B. 12
Here’s a step-by-step process for solving the problem:
1. Understand the problem: We are given that the exterior angle of a regular polygon is \(30^\circ\) and we need to find the number of sides (\(n\)) of this polygon.
2. Sum of exterior angles: The sum of all exterior angles of a polygon is always \(360^\circ\).
3. Formula for exterior angle: The measure of each exterior angle of a regular polygon is given by:
[tex]\[ \text{Exterior angle} = \frac{360^\circ}{n} \][/tex]
where \(n\) is the number of sides.
4. Set up the equation: Given the exterior angle is \(30^\circ\), we substitute this into the formula:
[tex]\[ 30^\circ = \frac{360^\circ}{n} \][/tex]
5. Solve for \(n\):
[tex]\[ n = \frac{360^\circ}{30^\circ} \][/tex]
6. Calculate the number of sides:
[tex]\[ n = 12 \][/tex]
Thus, the regular polygon has 12 sides. Therefore, the correct answer is:
B. 12
