The interior angles of regular polygon measure `150^(@)` each. The each number of diagonals of the polygon is

Explanation

Each of exterior angle`=30^(@)`
`therefore`Number of sides`=(360^(@))/(30^(@))=(360xx(pi)/(180))/(30xx(pi)/(180))=12`
`therefore`Number of diagonals`=.^(12)C_(2)-12=66-12=54`