[Hint: Draw a line parallel to ST through point R.]
NCERT Class 9 mathematics Chapter 6
Page No. 104
Exercise 6.2
Question No. 4
In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS.
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Contruction: Produce PQ, so that it intersect ST at M.
Given that: PQ||ST, therefore
∠1 = ∠2 [∵ Correspomding Angles]
⇒ ∠2 = 130°
∠2 + ∠3 = 180° [∵ Linear pair]
⇒ 130° + ∠3 = 180°
⇒ ∠3 = 180° – 130° = 50°
∠5 + ∠4 = 180° [∵ Linear pair]
⇒ 110° + ∠4 = 180°
⇒ ∠4 = 180° – 110° = 70°
In triangle QMR,
∠3 + ∠4 + ∠R = 180°
⇒ 50° + 70° + ∠R = 180°
⇒ 120° + ∠R = 180°
⇒ ∠R = 180° – 120° = 60°