Question

Please Answer Me This Immediately....

Answer 1

$\underline\mathfrak{\red{AnswEr}}$

In ∆XYZ,

Angle X=62°

Angle XYZ=54° .................... you have given in question (text)

angle X + angle xyz + angle Z = 180°............ angle addition property of triangle

62 + 54 + angle Z = 180°

116 + angle z = 180°

angle Z = 180 - 116

angle Z = 64°

OZ is angle bisector of angle XZY

angle OZY = 32°................1

similarly OY is angle bisector of angle XYZ

angle OYZ= 27°................... 2

in triangle OYZ,

angle OYZ+ angle OZY+ angle YOZ=180°............. angle sum property of triangle

27 + 32 + angle YOZ= 180

59 + angle YOZ = 180

angle YOZ= 121°

ANS: angle OZY=32°

angle YOZ= 121°

Answer 2

$\huge\red{\bold{\underline{\underline{Given:-}}}}$

• In ΔXYZ , ∠X = 62° , ∠Y = 54°
• YO and ZO are angular bisectors of ∠XYZ , ∠XZY

$\huge\blue{\bold{\underline{\underline{To\:Find:-}}}}$

• ∠OZY and ∠YOZ

$\huge\green{\bold{\underline{\underline{Solution:-}}}}$

∠X + ∠Y + ∠Z = 180° {From Angle sum property }

We have ,

• ∠X = 62°
• ∠Y = 54°

$\large\rm{\rightarrow{62+54+\angle\:Z\:=\:180}}$

$\large\rm{\rightarrow{116+\angle\:Z\:=\:180}}$

$\large\rm{\rightarrow{\angle\:Z\:=\:64}}$

Angular bisector are nothing but which seperates the one given angle into two equal parts .

This mean ,

∠XYO = ∠OYZ = Half of ∠Y and

∠XZO = ∠OZY = Half of ∠Z

Half of ∠Y = 54/2 = 27°

$\large\rm{\rightarrow{\angle\:XYO\:=\:27\:=\:\angle\:OYZ}}$

Half of ∠Z = 64/2 = 32°

$\large\rm{\rightarrow{\angle\:XZO\:=\:32\:=\:\angle\:OZY}}$

Now In ΔOYZ ,

∠OYZ + ∠YOZ + ∠OZY = 180° { from Angle sum property}

We have ,

• ∠OZY = 32°
• ∠OYZ = 27°

$\large\rm{\rightarrow{\angle\:YOZ+32+27\:=\:180}}$

$\large\rm{\rightarrow{\angle\:YOZ+59\:=\:180}}$

$\large\rm{\rightarrow{\angle\:YOZ\:=\:121}}$

∴ ∠YOZ = 121° and ∠OZY = 32°