Question

in the fig.if PQ II ST,<PQR=110°and <RST=130° then find the value of <QRS.

Answer 1

Draw a parallel line XY to PQ which passes through the point R.

Then,
Sum of interior angles on the same side of a transversal is 180°.
∠PQR + ∠QRX = 180°
110° + ∠QRX = 180°
∠QRX = 180° - 110°
∠QRX = 70°

∠TSR + ∠YRS = 180°
130° + ∠YRS = 180°
∠YRS = 180° - 130°
∠YRS = 50°

∠QRX + ∠YRS + ∠QRS = 180°
70° + 50° + ∠QRS = 180°
∠QRS = 180° - 120°
∠QRS = 60°