Question

Exterior angle of a regular polygon measures `10alpha` degrees.Then, prove that `alpha in ZZ` and there are precisely 7 such alpha#?

Answer 1

We know, the magnitude of each external angle of a regular polygon of `n` sides is related as follows.

Each external angle (`theta`) `=360^@/n`,where n must be an positive integer `>=3`.

Now it is given `theta=10alpha` degree

So `10alpha=360^@/n`

`=>alpha=36/n`

This shows that possible positive integral values of `alpha` are 12,9,6,4,3,2,1.

Hence `alpha inZZ` takes precisely 7 values.