# It is possible to design a regular polygon whose measures of each exterior angle is 50 . Yes /no give reason ?

##### 1 Answer
Jun 4, 2018

No, you cannot make a regular polygon with each exterior angle of ${50}^{\circ}$.

#### Explanation:

As we know, each exterior angle of a regular polygon (with $n$ sides) is equal and these angles add up to ${360}^{\circ}$.

$\text{exterior angle} \times n = {360}^{\circ}$

$\implies {50}^{\circ} \times n = {360}^{\circ}$

$\implies n = {360}^{\circ} / {50}^{\circ}$

$\implies n = 7.2$

Now, a polygon cannot have $7.2$ sides. Hence, the exterior angle of a regular polygon cannot be ${50}^{\circ}$.