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In the given fig. P, Q and R are three points on a circle  whose center is O and a tangent touches P. The extension part of QR and the tangent meet at a point of S. ∠PSQ = 45° and ∠RPS = 35°, find ∠QOR = ?

In the given fig. P, Q and R are three points on a circle  whose center is O and a tangent touches P. The extension part of QR and the tangent meet at a point of S. ∠PSQ = 45° and ∠RPS = 35°, find ∠QOR = ? Correct Answer 130° 

Given:

∠TPQ + ∠QPR + ∠RPS = 180° 

⇒ ∠QPR = 180° - (80° + 35°)

⇒ ∠QPR = 65° 

So, ∠QOR = 2 × ∠QPR

⇒ 2 × 65° = 130° 

∴ ∠QOR = 130° 

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