Question

Points P, Q, R and S lie on a circle. PQ = QR . If ∠ PQR = 116°, find ∠QSR

Answer 1

∠QSR = 32° if Points P, Q, R and S lie on a circle. PQ = QR .& ∠ PQR = 116°

Step-by-step explanation:

in Δ PQR

PQ = PR

=> ∠QPR = ∠QRP

∠PQR = 116°

∠PQR + ∠QPR + ∠QRP  = 180°

=>  116° + ∠QPR + ∠QRP  = 180°

=> ∠QPR + ∠QRP  = 64°

∠QPR = ∠QRP

=> ∠QPR = 32°

∠QSR = ∠QPR  ( angle subtended by same chord QR on same side of arc segment)

=> ∠QSR = 32°

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