Question

Angle x = 62°, angle xyz= 54° if yo and zo are bisectors of angle xyz and angle xzy resp. Find angle ozy and angle yoz

Answer 1

In triangle XYZ

angle X+angle Y + angle Z= 180( sum of triangle )

62°+54°+Z= 180

Z= 180-116

Z= 64

OZ is bisectors of angle Z

then 64/2

angle OZY= 32°

OY is bisectors of angle Y

then 54/2

angle OYZ= 27°

In triangle OYZ

angle O +Angle OYZ + angle OZY=180( total sum of triangle)

O+ 27+32 =180

O= 180-59

Angle O = 121°

Answer 2

Given: ∠X = 62°, ∠ XYZ = 54°

YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively.

To Find: ∠ OZY and ∠ YOZ.

Proof :

∠X + ∠XYZ + ∠XZY = 180°(Sum of the int. angles of a triangle = 180°)

=>62° + 54° + ∠XZY = 180°

=>116° + ∠XZY = 180°

=> ∠XZY = 64°

Now,

It is given that ZO is the bisector of ∠XZY

=>∠OZY = 1/2 ∠ XZY

=>∠OZY = 32°

Similarly

It is given that YO is bisector of ∠ XYZ

=>∠OYZ = 1/2 ∠XYZ

=>∠OYZ = 27°

Now,

∠OZY + ∠OYZ + ∠O = 180° (Sum of the int. angles of the triangle = 180°)

=>32° + 27° + ∠O = 180°

=>59° + ∠O = 180°

=>∠O = 121°