Question

in figure 6.40 angle x is equal to 62 degree angle x y z is equal to 54 degree if YO and Z O are bisector of angle xyz and angle x z y respectively of triangle xyz find angle o z y and angle YOZ​?​

Answer 1

Given :

• ∠XYZ = 54°
• ∠X = 62°

To Find :

• ∠OZY
• ∠YOZ

Solution :

$\longmapsto\tt{\angle{x}+\angle{y}+\angle{z}=180\degree\:(A.S.P)}$

$\longmapsto\tt{62\degree+54\degree+\angle{z}=180\degree}$

$\longmapsto\tt{\angle{z}=180\degree-116\degree}$

$\longmapsto\tt\bold{\angle{z}=64\degree}$

So ,

$\longmapsto\tt{\angle{OYZ}=\cancel\dfrac{54}{2}=27\degree}$

Similarly ,

$\longmapsto\tt{\angle{OZY}=\cancel\dfrac{64}{2}=32\degree}$

Now ,

In Δ YOZ :

$\longmapsto\tt{\angle{YOZ}+\angle{OYZ}+\angle{OZY}=180\degree\:(A.S.P)}$

$\longmapsto\tt{\angle{YOZ}+27\degree+32\degree=180\degree}$

$\longmapsto\tt{\angle{YOZ}+59\degree=180\degree}$

$\longmapsto\tt{\angle{YOZ}=180\degree-59\degree}$

$\longmapsto\tt\bold{\angle{YOZ}=121\degree}$