Question

In the adjoining figure x = 62°, xyz = 54°. If yo and zo
are the bisector of xyz and xzy respectively.
of xyz, find ozy and yoz.​

Answer 1

step 1 : Calculating xzy

xyz+zyx+xzy=180°

xzy=180°-54°-62°

xzy=64°

step 2: since O is the bisector so it will divide the angle in two equal part so

oyz=54/2= 27°

ozy=64/2 = 32°

step 3 : calculating yoz

yoz+ozy+ oyz=180°

yoz= 180°-32°-27°

yoz= 121°

Answer 2

Answer

( Given) In △xyz,  

∠x=62o

∠xyz=54o

OY is bisector of ∠xyz

OZ is bisector of ∠xzy

To find →∠ozy=?∠(yoz)=?

⇒ As we know, sum of angles of △=180o

∴∠YXZ+∠XYZ+∠XZY=180o

62+54+∠XZY=180

∠XZY=180−116

∠XZY=64o

As OZ is bisector of ∠xzy

∴∠OZY=2∠XZY​=264o​

∠OZY=32o​

⇒ Now, In △OZY,∠YOZ+∠OYZ+∠YZO=180o

∠YOZ+27+32=180o

∠YOZ=180−59

∠YOZ=21o​