The number id sides of a regular polygon whose exterior angles are each `72^@` is ?

Options

A. 7
B. 6
C. 5
D. 8

Answer

To find the number of sides of a regular polygon whose exterior angles are each \(72^\circ\), 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 1: Set up the equation
Given that the exterior angle is \(72^\circ\), we can set up the equation:

\[ 72^\circ = \frac{360^\circ}{n} \]

### Step 2: Rearrange the equation
To find \(n\), we can rearrange the equation:

\[ n = \frac{360^\circ}{72^\circ} \]

### Step 3: Calculate \(n\)
Now, we perform the division:

\[ n = \frac{360}{72} = 5 \]

### Conclusion
Thus, the number of sides of the regular polygon is \(5\).