एक नियमित बहुभुज के विकर्णों की संख्या ज्ञात कीजिए जिसमें प्रत्येक बाहरी कोण 24° है।

  1. 45
  2. 36
  3. 90
  4. 60

Answer (Detailed Solution Below)

Option 3 : 90
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दिया है :

प्रत्येक बाहरी कोण 24° है।

संकल्पना :

एक नियमित बहुभुज के बाहरी कोणों का योगफल = 360°

उपयोग किया गया सूत्र :
एक नियमित बहुभुज का प्रत्येक बाहरी कोण = 360/n

और

विकर्णों की संख्या = n(n – 3)/2

जहाँ n = भुजाओं की संख्या

गणना :

भुजाओं की संख्या = 360/24 = 15

इस प्रकार,

विकर्णों की संख्या = (15 × 12)/2 = 90
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