An exterior angle of a regular polygon is 24°. How many sides will the polygon have?

Question

Accepted Answer

1. **Formula for the exterior angle**:  
   The measure of each exterior angle of a regular polygon is given by:  
   $$
   	ext{Exterior Angle} = \frac{360}{n}
   $$  
   where $$ n $$ is the number of sides.

2. **Substitute the given value**:  
   Given that the exterior angle is **24°**, substitute into the formula:  
   $$
   24 = \frac{360}{n}
   $$

3. **Solve for $$ n $$**:  
   Multiply both sides by $$ n $$:  
   $$
   24n = 360
   $$  
   Divide both sides by 24:  
   $$
   n = \frac{360}{24} = 15
   $$

4. **Conclusion**:  
   The polygon has **15 sides**.

Thus, the correct answer is **(c) 15**.

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Answer

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