To determine the number of sides in a regular polygon with exterior angles that measure [tex]\( 60^\circ \)[/tex] each, let's follow these step-by-step instructions:
1. Understand the properties of the exterior angles of a polygon:
The sum of the exterior angles of any polygon, whether it is regular or not, is always [tex]\( 360^\circ \)[/tex].
2. Use the property of regular polygons:
In a regular polygon, all exterior angles are equal. If we let [tex]\( n \)[/tex] represent the number of sides of the polygon, the measure of each exterior angle is given by:
[tex]\[
\text{Exterior angle} = \frac{360^\circ}{n}
\][/tex]
3. Set up the equation with the given exterior angle:
According to the question, the measure of each exterior angle is [tex]\( 60^\circ \)[/tex]. Therefore, we can write the equation:
[tex]\[
\frac{360^\circ}{n} = 60^\circ
\][/tex]
4. Solve for [tex]\( n \)[/tex]:
Multiply both sides of the equation by [tex]\( n \)[/tex] to isolate [tex]\( 360^\circ \)[/tex] on the left side:
[tex]\[
360^\circ = 60^\circ \times n
\][/tex]
Then, divide both sides by [tex]\( 60^\circ \)[/tex]:
[tex]\[
n = \frac{360^\circ}{60^\circ} = 6
\][/tex]
Therefore, the number of sides in a regular polygon with each exterior angle measuring [tex]\( 60^\circ \)[/tex] is [tex]\( 6 \)[/tex].
So, the correct answer is:
B. 6
