The sum of the interior angles of a regular polygon is six times the sum of its exterior angles. Determine the number of diagonals in the polygon.
The sum of the interior angles of a regular polygon is six times the sum of its exterior angles. Determine the number of diagonals in the polygon.
एक समबहुभुज के आंतरिक कोणों का योग, उसके बाह्य कोणों के योग का छः गुना है। बहुभुज में विकर्णों की संख्या ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
77
Let the number of sides of the polygon be = n
Sum of interior angles =(n-2)$ \times180^\circ$
Sum of exterior angles =$ 360^\circ$
Given: (n-2) $ \times180=6\times360$
(n-2) $ \times180=2160$
n-2=12 = n=14
Number of diagonals = $ \frac{n(n-3)}{2}=\frac{14(14-3)}{2}=77$
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