Question
Download Solution PDFयदि एक सम बहुभुज में विकर्णों की संख्या 9 है, तो बहुभुज के सभी अंतः कोणों का योग क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
विकर्णों की संख्या = 9
प्रयुक्त सूत्र:
विकर्णों की संख्या = n(n - 3) / 2
आंतरिक कोणों का योग = (n - 2) × 180°
गणना:
⇒ n(n - 3)/2 = 9
⇒ n(n - 3) = 18
⇒ n2 - 3n - 18 = 0
⇒ (n - 6)(n + 3) = 0
⇒ n = 6 (चूँकि n > 0)
आंतरिक कोणों का योग = (6 - 2) × 180 = 4 × 180 = 720°
∴ सभी आंतरिक कोणों का योग = 720°
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