Question

In the figure, if PQ || ST, ∠PQR = 110° and ∠ RST = 130°, find ∠QRS.

Answer 1

Extend PQ to Y and draw LM || ST through R.

∠TSX = ∠QXS

[Alternate angles]

⇒ ∠QXS = 130°

∠QXS + ∠RXQ = 180°

[Linear pair axiom]

⇒ ∠RXQ = 180° – 130° = 50° …(1)

∠PQR = ∠QRM

[Alternate angles]

⇒ ∠QRM = 110° …(2)

∠RXQ = ∠XRM

[Alternate angles]

⇒ ∠XRM = 50° [By (1)]

∠QRS = ∠QRM – ∠XRM

= 110° – 50° = 60° Ans.