△ PQR లో, PQ మరియు PR భుజాలు E మరియు F వరకు విస్తరించబడ్డాయి, అంటే ∠Q మరియు ∠R యొక్క బాహ్య కోణం ద్విపది బిందువు k వద్ద కలుస్తుంది. ∠QPR = 110° అయితే, ∠QKR =?

  1. 55°
  2. 45°
  3. 25°
  4. 35°

Answer (Detailed Solution Below)

Option 4 : 35°
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Detailed Solution

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F1Ashish.k 05-10-20 Savita D4

ఇచ్చినది:

∠QPR = 110°

సూత్రం:

త్రిభుజం యొక్క మూడు కోణాల మొత్తం 180°

∠QKR = 90° - ∠QPR/2

లెక్కింపు:

∠RQK = (180° - ∠PQR)/2

∠QRK = (180° - ∠PRQ)/2

△QKRలో

∠RQK + ∠QRK + ∠QKR = 180°

⇒ [(180° - ∠PQR)/2] + [(180° - ∠PRQ)/2] + ∠QKR = 180°

⇒ 90° - [∠PQR/2] + 90 – [∠PRQ/2] + ∠QKR = 180°

⇒ 180 – [(∠PQR + ∠PRQ)/2] + ∠QKR = 180

⇒ ∠QKR = (∠PQR + ∠PRQ)/2

⇒ 2∠QKR = ∠PQR + ∠PRQ

⇒ 2∠QKR = 180° - ∠QPR

⇒ 2∠QKR = 180° - 110

⇒ ∠QKR = 70/2

∴ ∠QKR = 35°

చిన్న చిట్కా:

ఇక్కడ, K అనేది ΔPQR యొక్క బాహ్య బిందువు, కావున ∠QKR = 90° - (∠QPR/2)

∠QKR = 90° - 110°/2

∴ ∠QKR = 90° - 55° = 35°

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