The interior angles of a regular polygon measure `150^@` each. The 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`