If the measure of the exterior angle of a regular polygon is `72^(@)` then how many sides does it have?

Options

A. 6
B. 8
C. 9
D. 5

Answer

To find the number of sides of a regular polygon given that the measure of its exterior angle is \(72^\circ\), we can use the formula for the exterior angle of a regular polygon:

\[ \text{Exterior Angle} = \frac{360^\circ}{n} \]

where \(n\) is the number of sides of the polygon.

### Step-by-step Solution:

1. **Set up the equation using the given exterior angle**:
Given that the exterior angle is \(72^\circ\), we can set up the equation:
\[ \frac{360^\circ}{n} = 72^\circ \]

2. **Cross-multiply to solve for \(n\)**:
To eliminate the fraction, we can cross-multiply:
\[ 360^\circ = 72^\circ \cdot n \]

3. **Isolate \(n\)**:
Now, we need to isolate \(n\) by dividing both sides by \(72^\circ\):
\[ n = \frac{360^\circ}{72^\circ} \]

4. **Calculate the value of \(n\)**:
Now, we can perform the division:
\[ n = 5 \]

5. **Conclusion**:
The number of sides of the polygon is \(5\).

### Final Answer:
The regular polygon has **5 sides**.