In the given figure,

∠X = 62° and ∠XYZ = 54°

∠XYZ + ∠XZY + ∠YXZ = 180° …(i)

[Angle sum property of a triangle]

⇒ 54° + ∠XZY + 62° = 180°

⇒ ∠XZY + 116° = 180°

⇒ ∠XZY = 180° – 116° = 64°

Now, ∠OZY = 1/ 2 × ∠XZY [∵ZO is bisector of ∠XZY]

= 1 /2 × 64° = 32°

Similarly, ∠OYZ = 1/2 × 54° = 27°

Now, in ∆OYZ, we have

∠OYZ + ∠OZY + ∠YOZ = 180° Angle sum property of a triangle]

⇒ 27° + 32° + ∠YOZ = 180°

⇒ ∠YOZ = 180° – 59° = 121°

Hence, **∠OZY = 32° and ∠YOZ = 121° Ans.**