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

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The interior angles of a regular polygon measure `150^@` each. The number of diagonals of the polygon is
A. `35`
B. `44`
C. `54`
D. `78`


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Correct Answer - C
`(c )` We have `pi-(2pi)/(n)=(5pi)/(6)`
`implies (pi)/(6)=(2pi)/(n)`
`impliesn=12`
`:.` Number of diagonals `="^(10)C_(2)-12=54`

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