ஒரு நாற்கர ABCD இல், ∠C மற்றும் ∠D இன் இருபிரிவுகள் E இல் சந்திக்கின்றன. ∠CED = 43° மற்றும் ∠A = 32° எனில், ∠B இன் அளவு∶

  1. 34°
  2. 54°
  3. 55°
  4. 60°

Answer (Detailed Solution Below)

Option 2 : 54°
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Detailed Solution

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குறுகிய தந்திரம்∶

நாம் அறிந்தபடி,

∠A + ∠B = 2∠CED

⇒ 32° + ∠B = 2 × 43°

⇒ ∠B = 86° – 32° = 54°

விரிவான தீர்வு∶

F1 Madhuri SSC 19.04.2022 D2

ΔCED இல்

∠C/2 + ∠D/2 + ∠CED = 180°

⇒ ∠C/2 + ∠D/2 + 43° = 180°

⇒ ∠C/2 + ∠D/2 = 180° – 43° = 137°

⇒ ∠C + ∠D = 137° × 2 = 274°

நாம் அறிந்தபடி,

∠A + ∠B + ∠C + ∠D = 360°

⇒ 32° + ∠B + 274° = 360°

⇒ ∠B = 360° – 306° = 54°

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