PQ and PR PQ and PR are the tangents to circle with Centre O and S is the point on the circle such that angle SQL is equals to 50 degree and Angle SSRM is equal to 60 degree then find angle qsr
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Hey there!
Let T be the point on the circle such that QT and RT meet at T.
Using the Alternate Segment Theorem, ∠QTS = 50° and ∠RTS = 60°
Thus,
∠QTR = ∠QTS + ∠RTS
= 60° + 50°
= 110°
Quadrilateral is Cyclic
Hence Opposite angles are Supplementary
⇒ ∠QRS+∠QTR = 180°
⇒ ∠QRS+110° = 180°
⇒ ∠QRS = 70°
HOPE IT HELPED ^_^
Let T be the point on the circle such that QT and RT meet at T.
Using the Alternate Segment Theorem, ∠QTS = 50° and ∠RTS = 60°
Thus,
∠QTR = ∠QTS + ∠RTS
= 60° + 50°
= 110°
Quadrilateral is Cyclic
Hence Opposite angles are Supplementary
⇒ ∠QRS+∠QTR = 180°
⇒ ∠QRS+110° = 180°
⇒ ∠QRS = 70°
HOPE IT HELPED ^_^
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