Question
Download Solution PDFदी गई आकृति में, AB = DB और AC = DC है। यदि ∠ABD = 58° और ∠DBC = (2x - 4)°, ∠ACB = (y + 15)° और ∠DCB = 63° है, तब 2x + 5y का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
AB = DB और AC = DC,
∠ABD = 58° और ∠DBC = (2x - 4)°,
∠ACB = (y + 15)° और ∠DCB = 63°
प्रयुक्त अवधारणा:
यदि एक त्रिभुज की तीनों भुजाएँ दूसरे त्रिभुज की संगत तीन भुजाओं के बराबर हों, तो SSS (भुजा-भुजा-भुजा) नियम के अनुसार दोनों त्रिभुज सर्वांगसम कहलाते हैं।
गणना:
चूँकि AB = DB, AC = DC है और BC दोनों त्रिभुजों के लिए उभयनिष्ठ है।
इसलिए, ΔABC ≅ ΔDBC
इसलिए, ∠ABC = ∠DBC = ∠ABD/2
⇒ 58°/2 = 29°
इसलिए,
(2x - 4)° = 29°
⇒ 2x = 33°
पुनः,
∠ACB = ∠DCB = 63°
इसलिए,
(y + 15)° = 63°
⇒ y = 48°
इसलिए,
2x + 5y = 33° + 5 × 48°
⇒ 33° + 240°
⇒ 273°
∴ अभीष्ट उत्तर 273° है।
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