Question

∠X = 62°, ∠XYZ = 54°. lfYO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of Δxyz, find ∠OZY and ∠YOZ. In Fig. 6.40.

Answer 1

YOZ=121 OZY=32=1/2 XYZ

Answer 2

Hello mate ☺

____________________________

Solution:

In ∆XYZ, we have

∠XYZ+∠XZY+∠X=180°    (Sum of three angles of a triangle =180°)

⇒540+∠XZY+62°=180°

⇒∠XZY=180°−54°−62°=64°

It is given that OY and OZ are bisectors of ∠XYZ and ∠XZY respectively

Therefore, ∠OZY=1/2(∠XZY)

=1/2(64°)

=32°

Similarly, ∠OYZ=1/2(∠XYZ)

=1/2(54°)

=27

In ∆OYZ, we have

∠OYZ+∠OZY+∠YOZ=180°  (Sum of three angles of a triangle =180°)

⇒27°+32°+∠YOZ=18°

⇒∠YOZ=180°−27°−32°=121°

Therefore, ∠OZY=32° and ∠YOZ=121°

I hope, this will help you.☺

Thank you______❤

_____________________________❤