in the following figure PQ and PR are tangent at Q and R respectively. if angle SQR =38° then find angle QPR angle PRQ angle QSR and angle PQR
Answers
Given : .PQ and PR are tangents at Q and R, respectively.
S is center of circle
∠SQR = 38°,
To Find : ∠QPR, ∠PRQ, ∠QSR and ∠PQR
Solution:
∠SQR = 38°
∠SRQ = 38° ∵ SQ = SR = Radius
∠SQR + ∠SRQ + ∠QSR = 180° ( sum of angles of triangle )
=> 38° + 38° + ∠QSR = 180°
=> ∠QSR = 104°
∠QSR + ∠SQP + ∠SRP + ∠QPR = 360° ( sum of angles of quadrilateral )
=> 104° + 90° + 90° + ∠QPR = 360°
=> ∠QPR =76°
∠SQR = 38° ∠SQR + ∠PQR = 90° => ∠PQR =52°
∠SRQ = 38° ∠SRQ + ∠PRQ= 90° => ∠PRQ =52°
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