Question

In figure.6.40, angle X = 62 °,angle XYZ=54°. If YO and ZO are the bisectors of angle XYZ and angle XYZ respectively of triangle XYZ,find angle OZY and angle YOZ.

Answer 1

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

Answer= angle ozy = 32° and angle yoz = 121°.

Step-by-step explanation:

In triangle xyz,

Angle x = 62°

Angle xyz = 54°

Angle x + angle xyz + angle z = 180° [by 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 xyz

Angle ozy = 32° •••••••••• (1) eq

Similarly oz is the angle bisector of angle xyz

Angle oyz = 27°••••••••••(2) eq

In triangle oyz,

Angle oyz + ozy + yoz = 180°[ by angle sum property of triangle]

27°+32°+ angle yoz = 180°

59°+angle yoz=180°

Angle yoz = 180°+59°

Angle yoz = 121°

Therefore, angle ozy =32° and angle yoz = 121°

I hope this answer will help you.

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