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 को योग, उसके बाह्य कोणों के योग का छः गुणा है। बहुभुज में विकर्णों की संख्या ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
77
Sum of exterior angles=$ 360^\circ$
Sum of interior angles = $6\times360^\circ=2160^\circ$
$(n-2)\times 180=2160$
n-2=12
n=14
$\text{Number of diagonals}=\dfrac{n(n-3)}{2}$
$=\dfrac{14(14-3)}{2}$
$=\dfrac{14\times11}{2}$
Correct Answer: 77 ✅
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