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

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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.

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