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  • Solve it, The interior angles of a regular polygon measure 150° each. The number of diagonals of the polygon is:

The interior angles of a regular polygon measure 150° each. The number of diagonals of the polygon is:

  • Option 1)

    35

  • Option 2)

    44

  • Option 3)

    54

  • Option 4)

    78

 

Answers (1)

As learnt in concept

Geometrical Permutations -

The number of diagonals of n sided convex polygon is ^{n}c_{2}-n=\frac{n(n-3)}{2}.

- wherein

Where n > 3

 

 The interior angle=\frac{(n-2)\times180^\circ}{n}=150^\circ

\frac{n-2}{n}=\frac{5}{6}

Thus n=12

number\ of\ diagonals =\frac{n(n-3)}{2}

\frac{12\times9}{2}=54


Option 1)

35

This is incorrect option

Option 2)

44

This is incorrect option

Option 3)

54

This is correct option

Option 4)

78

This is incorrect option

Posted by

Vakul

View full answer

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