Question
Download Solution PDF△ 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 =?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFఇచ్చినది:
∠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°
Last updated on Jul 10, 2025
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