Question

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

Answer 1

In ΔPQR, We have
PQ = PR
⇒ ∠ PQR = ∠ PRQ
⇒ ∠ PRQ = 35°
∴ ∠ QPR = 180° - ( ∠ PQR + ∠ PRQ)
∴ ∠ QPR = 180° - ( 35° + 35°) = 110°

Since PQTR is a cyclic quadrilateral.
∴ ∠ P + ∠ T = 180°
∴ ∠ T = 180° - 110° = 70°.

In cyclic quadrilateral QSRT, we have
∴ ∠ S + ∠ T = 180°
⇒  ∠ S = 180° - 70° = 110°.