Question
Download Solution PDFयदि सम बहुभुज के प्रत्येक बाहरी कोण 24° हैं, तो सम बहुभुज में कितनी भुजाएं हैं?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
n भुजाओं वाला बहुभुज,
- आंतरिक कोण + बाहरी कोण = 180°
- बहुभुज का प्रत्येक आंतरिक कोण = \(\rm \left ( n-2 \right )\times \frac{180^{0}}{n}\) .
गणना:
हम जानते हैं कि, आंतरिक कोण + बाहरी कोण = 180°
⇒ आंतरिक कोण + 24° = 180°
⇒ आंतरिक बहुभुज का कोण = 156°
∴ 156 = \(\rm \left ( n-2 \right )\times \frac{180^{0}}{n}\)
⇒ 26n = 30n - 60
⇒ 4n = 60
⇒ n = 15
सही विकल्प 3 है।
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