The exterior angle of a regular polygon is one-third of its interior angle. How many sides has the polygon?

Explanation

Let interior angle is x^@
then its exterior angle `=x/3`
according to question
exterior angle`=180^@-`interior angle
`x^@/3=180^@-x^@`
`x^@+x^@/3=180^@`
`4x/3=180^@`
`x=135^@`
interior angle`=(n-2)xx180/n`
`135^@=(n-2)xx180^@/n`
`3n=4n-8`
`n=8`