नीचे दी गई आकृति में, ∠ACB = 80°, ∠BAC = 45° और ∠BED = 75°, तो ∠BDE का मान ज्ञात कीजिए।

F1 M.S 27.7.20 Pallavi D3

  1. 50°
  2. 75°
  3. 45°
  4. 90°

Answer (Detailed Solution Below)

Option 1 : 50°
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दिया है:

∠ACB = 80°, ∠BAC = 45° और ∠BED = 75°

संकल्पना:

एक त्रिभुज के सभी कोणों का योगफल = 180°

गणना:

F1 M.S 27.7.20 Pallavi D3

ΔABC में:

∠BAC + ∠ACB + ∠CBA = 180°

⇒ ∠CBA = 180° – 80° – 45° = 55°

इस प्रकार,

∠DBE = ∠CBA = 55° (विपरीत कोण)

अब,

∠BDE + ∠DEB + ∠DBE = 180°

⇒ ∠BDE = 180° – 75° – 55° = 50°

∴ ∠BDE = 50°

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