The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides of the polygon.

Explanation

Given: The sum of the interior angles of a polygon is three times the sum of its exterior angles.
Sum of all interior angles of a regular polygon`=180^@(n−2)`, where `n` is number of sides of a polygon
Sum of all exterior angle of a regular polygon`=360^@`
According to question,`180^@(n−2)=3xx360^@`
`=>(n−2)=6`
`=>n=8`
Hence, the number of sides of the polygon is `8`.