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
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°