It is possible to have a regular polygon having each exterior angle as 75 o . Mark True / False.

1. Break Down the Problem

To determine if it's possible to have a regular polygon with each exterior angle measuring $75^\circ$, we need to analyze the properties of exterior angles of polygons.

2. Relevant Concepts

The formula for the measure of each exterior angle of a regular polygon is given by:

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

where $n$ is the number of sides of the polygon.

3. Analysis and Detail

We can set the exterior angle equal to $75^\circ$ and solve for $n$:

$75^\circ = \frac{360^\circ}{n}$

To find $n$, we can rearrange the equation:

$n = \frac{360^\circ}{75^\circ}$

4. Verify and Summarize

Now, performing the calculation:

$n = \frac{360}{75} = 4.8$

Since $n$ must be a whole number (polygons have a finite number of sides), $n = 4.8$ is invalid.

Final Answer

Thus, it is False that a regular polygon can have each exterior angle as $75^\circ$.