दी 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?

F1 SSC Ishita 24.02.23 D1

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SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 4)
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  1. 325°
  2. 273°
  3. 259 °
  4. 268°

Answer (Detailed Solution Below)

Option 2 : 273°
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दिया 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:

F1 SSC Ishita 24.02.23 D2

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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