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The interior angles of polygon measure 150 degree each. The number of diagonals of the polygon is_______ (A) 35 (B) 44 (C) 54 (D) 78 Please explain step by step.

The interior angles of polygon measure 150 degree each. The number of diagonals of the polygon is_______
(A) 35
(B) 44
(C) 54
(D) 78
Please explain step by step.

Grade:11

1 Answers

Sunil Raikwar
askIITians Faculty 45 Points
8 years ago
each interior angle of a regular polygon=(n-2).180/n
(n-2).180=150n
6n-12=5n
n=12
no. of diagonal=n(n-3)/2=12x9/2=54

Thanks & Regards
Sunil Raikwar
askIITians Faculty

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