Question

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

Answer 1

Given that ∠X = 62° and ∠Y = 54° 

YO arid ZO are bisectors of ∠Y and ∠Z. 

In ΔXYZ 

∠X + ∠XYZ + ∠XZY = 180° . 

62° + 54° + ∠XZY = 180° 

=> ∠XZY = 180°- 116° = 64° 

Also in ΔOYZ 

∠OYZ = 1/2 ∠XYZ = 1/2 x 54° = 27° 

(∵ YO is bisector of ∠XYZ) 

∠OZY = 1/2 ∠XZY = 1/2 x 64° = 32 

(∵ OZ is bisector of ∠XYZ) 

And ∠OYZ + ∠OZY + ∠YOZ = 180°

(∵ angle sum property, ΔOYZ) 

⇒ 27 + 32° + ∠YOZ = 180° 

⇒ ∠YOZ = 180° – 59° = 121°