Question

Is it possible to have a regular polygon with measure of each exterior angle as ${58}^o$ why? Can it be an interior angle of a regular polygon ?

Answer 1

We know that each exterior angle of regular polygon is given by $\frac{360}{n}$

then, $\frac{360}{n}=58$

$n=\frac{180}{29}$

Which is not a natural number

It is not possible to have a regular polygon with each exterior angle as ${58}^{\circ }$

Also,

We know that each interior angle of a regular polygon is given by

$\frac{(n-2)}{n}\times 180$

So, $\left(\frac{n-2}{n}\right)\times 180=58$

$n=\frac{180}{61}$

which is not natural number

Therefore, ${58}^{\circ }$ cannot be an interior angle of a regular polygon.