Question
Download Solution PDFఒకవేళ బహుభుజి యొక్క బాహ్య కోణం 45° అయితే, ఆ బహుభుజిలో ఉన్న కర్ణాల సంఖ్య ఎంతో కనుక్కోండి.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇవ్వబడింది:
బాహ్యకోణం = 45°
వాడిన సూత్రం:
బాహ్యకోణం = (360°/n)
n భుజాలున్న బహుభుజి యొక్క కర్ణాల సంఖ్య= (n2 - 3n)/2
ఇక్కడ, n = బహుభుజి భుజాల సంఖ్యకి సమానం
లెక్క:
బాహ్యకోణం = (360°/n)
⇒ 45° = (360°/n)
⇒ n = 8
ఇప్పుడు, 'n' భుజాలున్న బహుభుజి యొక్క కర్ణాల సంఖ్య
⇒ (n2 - 3n)/2
⇒ (64 - 24)/2
⇒ 20
∴ కర్ణాల సంఖ్య 20.
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