Question

In Fig. 16.177, Δ PQR is an isosceles triangle with PQ=PR and m∠PQR=35°. Find m∠QSR and m∠QTR.

Answer 1

m∠QSR =   110° , m∠QTR =   70°

Step-by-step explanation:

Δ PQR is an isosceles triangle with PQ=PR

=> ∠PQR = ∠PRQ  = 35°

in Δ PQR

∠QPR + ∠PQR + ∠PRQ = 180°

=>∠QPR + 35°  + 35°  = 180°

=> ∠QPR  = 110°

∠QSR = ∠QPR  ( angle by sanme chord AR in same arc segment)

=> ∠QSR =   110°

m∠QSR =   110°

QSRT is cyclic quadrilateral

=> ∠QSR + ∠QTR = 180°  ( Sum of opposite angles of cyclic quadrilateral)

=> 110° + ∠QTR = 180°

=> ∠QTR  = 70°

m∠QTR =   70°

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Answer 2

∠QTR = 110

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