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

YXZ +XYZ + XZY =180°

62° +54° +XZY = 180°

XZY=180°-62°-54°

XZY =64°

2OZY =64°

OZY=64°/2=32°..................(1)

in the OZY OYZ +OZY +YOZ = 180°

54°/2 +32° +YOZ = 180°

YOZ = 180°- 32° - 27°
YOZ =121°...............(2)

Answer 2

Answer:

∠OZY=32°

∠YPZ=121°

Step-by-step explanation:

In ΔXYZ, ∠X+∠Y+∠Z=180°........ (1)

Given that, ∠X=62° and ∠Y=54°

Hence, from equation (1) ∠Z=180°-62°-54° =64°

Now, since ZO is the bisector of ∠Z.

Hence, ∠OZY =1/2(∠Z)=1/2(64°)=32° ........ (2) (Answer)

Again, ∠OYZ =1/2(∠Y)=1/2(54°) =27° ........ (3)

{Since, YO is the bisector of ∠Y}

In ΔOYZ, ∠OZY+∠OYZ+∠YOZ =180°

⇒ 32° +27° +∠YOZ =180° {From equations (2) and (3).}

⇒ ∠YOZ= 180°-32°-27° =121° (Answer)