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

Given, ∠X = 62°, ∠XYZ = 54°
YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively.
According to the question
∠X + ∠XYZ + ∠XZY = 180° (Sum of the interior angles of the triangle)
⇒ 62° + 54° + ∠XZY = 180°
116° + ∠XZY = 180°
∠XZY = 64°
Now, ∠OZY = ½∠XZY (ZO is the bisector)
⇒ ∠OZY = 32°
Also ∠OYZ = ½∠XYZ (YO is the bisector)
⇒ ∠OYZ = 27°
Now, ∠OZY + ∠OYZ + ∠YOZ = 180° (Sum of the interior angles of the triangle)
⇒ 32° + 27° + ∠YOZ = 180°
⇒ 59° + ∠YOZ = 180°
⇒ ∠YOZ = 121°