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jimmy389
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Asked: 2023-03-24T06:46:11+00:00 In:

In Fig. 6.42, if lines PQ and RS intersect at point T, such that ∠ PRT = 40°, ∠ RPT = 95° and ∠ TSQ = 75°, find ∠ SQT.

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In Fig. 6.42, if lines PQ and RS intersect at point T, such that ∠ PRT = 40°, ∠ RPT = 95° and ∠ TSQ = 75°, find ∠ SQT.

Exercise 6.3 of Class 9 Maths Chapter 6 Lines and Angles introduces important terms such as exterior angle, linear pair and vertically opposite angles, requiring students to practice this exercise.

NCERT Class 9 Chapter 6 Exercise 6.3 Question No. 4
Page No. 107 & 108

chapter 6class 9ncert maths
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      Given that: ∠PRT = 40°, ∠RPT = 95° and ∠TSQ = 75°
      In △PTR, ∠P + ∠R + ∠PTR = 180°
      ⇒ 95° + 40° + ∠PTR = 180°
      ⇒ 135° + ∠PTR = 180°
      ⇒ ∠PTR = 180° – 135° = 45°
      ∠STQ = ∠PTR [∵ Vertically Opposite Angles]
      ⇒ ∠STQ = 45°
      In △SQT, ∠STQ + ∠S + ∠SQT = 180°
      ⇒ 45° + 75° + ∠SQT = 180°
      ⇒ 120° + ∠SQT = 180°
      ⇒ ∠SQT = 180° – 120° = 60°

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