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jimmy389
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Asked: 2023-03-24T06:45:52+00:00 In:

In Fig. 6.40, ∠ X = 62°, ∠ XYZ = 54°. If YO and ZO are the bisectors of ∠ XYZ and ∠ XZY respectively of ∆ XYZ, find ∠ OZY and ∠ YOZ.

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In Fig. 6.40, ∠ X = 62°, ∠ XYZ = 54°. If YO and ZO are the bisectors of ∠ XYZ and ∠ XZY respectively of ∆ XYZ, find ∠ OZY and ∠ YOZ.

Important theorems and properties related to parallel lines, transversal lines, alternate angles, equivalent angles, interior angles, and exterior angles are covered in class 9 NCERT math chapter 6 exercise 6.3.

NCERT CLASS 9 Chapter 6 Exercise 6.3 Lines and Angles Question No.2
Page No. 107

chapter 6mathsncert class 9
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      Given that : ∠X = 62° and ∠XYZ = 54°
      In △XYZ, ∠X + ∠XYZ + ∠XZY = 180°
      ⇒ 62° + 54° + ∠XZY = 180°
      ⇒ 116° + ∠XZY = 180°
      ⇒ ∠XZY = 180° – 116° = 64°
      YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively. therefore,
      ∠OYZ = 1/2 ∠XYZ = 1/2 × 54° = 27°
      ∠OYZ = 1/2 ∠XZY = 1/2 × 64° = 32°
      In △OYZ, ∠OZY + ∠OYZ + ∠YOZ = 180°
      ⇒ 32° + 27° + ∠YOZ = 180°
      ⇒ 59° + ∠YOZ = 180°
      ⇒ ∠YOZ = 180° – 59° = 121°

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