Question

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

Answer 1

In this figure, 

∠X = 62° 

∠XYZ = 54° 

In ∆XYZ, YO and ZO are angular bisectors of 

∠XYZ and ∠XZY. 

Then, ∠OZY = ? ∠OYZ = ?

In ∆XYZ 

∠X + ∠Y + ∠Z = 180° 

62 + 54 + ∠Z= 180 

116 + ∠Z= 180 ∠Z= 180- 116 

∴ ∠Z = 64° YO is the angular bisector of ∠Y 

∴ ∠OYZ = = 27° 

ZO is the angular bisector of ∠Z 

∴ ∠OZY = = 32° 

∴ ∠OZY = 32° 

Now, in ∆OYZ, 

∠OYZ + ∠OZY + ∠YOZ = 180° 

27 + 32 + ∠YOZ = 180 

59 + ∠YOZ = 180 

∠YOZ = 180 – 59 

∴∠YOZ = 121° 

∴ ∠OZY = 32° 

∠YOZ = 121°