Question
Download Solution PDFसमबाहु ΔABC में, D और E क्रमशः AB और AC की भुजाओं पर बिंदु हैं जैसे कि AD = CE हैं। BE और CD, F पर प्रतिच्छेद करते हैं। तो ∠CFB का माप क्या (डिग्री में) है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया हैं:
D और E भुजाओं AB और AC पर स्थित बिंदु हैं।
AD = CE
BE और CD, F पर प्रतिच्छेद करते हैं।
प्रयुक्त अवधारणा:
त्रिभुज की सर्वांगसमता की अवधारणा,
बहिष्कोण हमेशा अंतराभिमुख कोण के योग के बराबर होता है।
गणना:
ΔCBE ≅ ΔACD [SAS सर्वांगसमता]
तो, इन दोनों त्रिभुजों के तीनों कोण समान हैं,
माना कि ∠EBC, θ हैं इसमे से ∠ACD भी θ हैं।
अब,
∠BEC = 180° - (60° + θ)
⇒ 120° - θ
अब, ΔECF में
बहिष्कोण ∠CFB = (120° - θ) + θ
⇒ 120°
∴ ∠CFB, 120° हैं।
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