Question

In following figure , Δ PQR is an isosceles teiangle with PQ = PR and m ∠ PQR = 35° .Find m ∠ QSR and ∠ QTR 

Answer 1

In  Δ PQR., 

PQ = PR

∴ ∠ PQR = ∠ PRQ = 35°

Also , ∠ PQR + ∠ PRQ  + ∠QPR = 180°

35 + 35 +  ∠QPR = 180

∠QPR = 110°

In cyclic quadrilateral PQSR ,

∠QPR + ∠QSR = 180

110 + ∠QSR = 180

∠QSR = 70

Also , ∠QSR = ∠QTR = 70°  (Angles in the same segment)