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ballu43
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Asked: 2023-03-23T11:36:27+00:00 In:

In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS.

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In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS.

[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

chapter 6class 9ncert
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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°

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