Answer :
To determine the number of sides of a regular polygon given its exterior angle measures [tex]$30^{\circ}$[/tex], we can use the properties of polygons.
1. Exterior Angles of a Polygon:
- The sum of the exterior angles of any polygon is always [tex]$360^{\circ}$[/tex].
2. Finding the Number of Sides:
- If each exterior angle of a regular polygon is [tex]$30^{\circ}$[/tex], we can use the formula for the sum of the exterior angles to find the number of sides.
- The formula for the number of sides [tex]\( n \)[/tex] of a regular polygon can be derived from:
[tex]\[ \text{Number of sides} = \frac{\text{Sum of exterior angles}}{\text{Measure of one exterior angle}} \][/tex]
3. Applying the Values:
- The sum of the exterior angles is [tex]$360^{\circ}$[/tex]. The measure of one exterior angle is given as [tex]$30^{\circ}$[/tex].
- Plug in these values into the formula:
[tex]\[ n = \frac{360^{\circ}}{30^{\circ}} \][/tex]
4. Calculation:
- Perform the division:
[tex]\[ n = 12 \][/tex]
Therefore, the number of sides of the regular polygon is 12.
The correct answer is:
A. 12
1. Exterior Angles of a Polygon:
- The sum of the exterior angles of any polygon is always [tex]$360^{\circ}$[/tex].
2. Finding the Number of Sides:
- If each exterior angle of a regular polygon is [tex]$30^{\circ}$[/tex], we can use the formula for the sum of the exterior angles to find the number of sides.
- The formula for the number of sides [tex]\( n \)[/tex] of a regular polygon can be derived from:
[tex]\[ \text{Number of sides} = \frac{\text{Sum of exterior angles}}{\text{Measure of one exterior angle}} \][/tex]
3. Applying the Values:
- The sum of the exterior angles is [tex]$360^{\circ}$[/tex]. The measure of one exterior angle is given as [tex]$30^{\circ}$[/tex].
- Plug in these values into the formula:
[tex]\[ n = \frac{360^{\circ}}{30^{\circ}} \][/tex]
4. Calculation:
- Perform the division:
[tex]\[ n = 12 \][/tex]
Therefore, the number of sides of the regular polygon is 12.
The correct answer is:
A. 12
