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  • The interior angles of a regular polygon measure each The number of diagonals of the polygon is</

The interior angles of a regular polygon measure 150^{\circ} each The number of diagonals of the polygon is

Option: 1

35


Option: 2

44


Option: 3

54


Option: 4

78


Answers (1)

best_answer

We have \pi-\frac{2 \pi}{n}=\frac{5 \pi}{6}

\begin{aligned} & \Rightarrow \quad \frac{\pi}{6}=\frac{2 \pi}{n} \\ \\& \Rightarrow \quad n=12 \end{aligned}

\therefore Number of diagonals ={ }^{10} C_2-12=54

 

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Ritika Jonwal

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