Question
Download Solution PDFΔABC में, लंब AG, BH और CI, O पर मिलते हैं। यदि ∠B = 44°, ∠C = 66°, तो ∠BOC का माप ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
ΔABC में, लंब समद्विभाजक AG, BH और CI, O पर मिलते हैं।
∠B = 44°, ∠C = 66°
प्रयुक्त अवधारणा:
त्रिभुज के सभी तीन कोणों का योग 180° है।
वे बिंदु जहाँ लंबवत मिलते हैं, वह है लंबकेंद्र।
दी गई भुजा से लंबकेंद्र पर बनने वाला कोण = [180 ° - (दी गई भुजा के विपरीत कोण)]
गणना:
त्रिभुज के समकोण गुण (सम एंगल प्रॉपर्टी) के अनुसार,
∠A + ∠B + ∠C = 180°
⇒ ∠A + 44° + 66° = 180°
⇒ ∠A = 180° - 110°
⇒ ∠A = 70°
दी गई भुजा से लंबकेंद्र पर बनने वाला कोण = [180 ° - (दी गई भुजा के विपरीत कोण)]
⇒ ∠BOC = 180° - 70° = 110°
∴ ∠BOC 110° के बराबर है।
Confusion Pointsदिया गया बिंदु लंबकेंद्र है, लंबकेंद्र के गुण के अनुसार,
लम्बकेंद्र पर बना कोण = [180° - (दी गई भुजा के विपरीत कोण)]
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