ఒక చక్రీయ చతుర్భుజి PQRSలో, ∠PQR మరియు ∠QRS కోణాలు 30° మరియు 50° గా ఉంటాయి. ∠SPQ మరియు ∠RSP కోణాల మధ్య తేడా ఏంటి?

  1. 30° 
  2. 50°
  3. 20°
  4. 80°

Answer (Detailed Solution Below)

Option 3 : 20°
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Detailed Solution

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ఇవ్వబడింది:

∠PQR = 30°

∠QRS = 50°

వాడిన కాన్సెప్ట్:

చక్రీయ ఛతుర్భుజిలో, 

ఎదురు కోణాల మొత్తం = 180° 

లెక్క:

∠PQR + ∠RSP = 180°      (∵ ఎదురుకోణాల మొత్తం = 180°)

⇒ 30° + ∠RSP = 180°

⇒ ∠RSP = 150°

∠QRS + ∠SPQ = 180°      (∵ ఎదురుకోణాల మొత్తం = 180°)

⇒ 50° + ∠SPQ = 180°

⇒ ∠SPQ = 130°

⇒ ∠RSP - ∠SPQ  = 20°

∴ ∠SPQ మరియు ∠RSP కోణాల మధ్య తేడా 20°.

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