Question

Is it possible to have a regular polygon with measure of each interior angle as 580°? 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

n

360

then,

n

360

=58

n=

29

180

Which is not a natural number

It is not possible to have a regular polygon with each exterior angle as 58

∘

Also,

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

n

(n−2)

×180

So, (

n

n−2

)×180=58

n=

61

180

which is not natural number

Therefore, 58

∘

cannot be an interior angle of a regular polygon.