Question

2) In this fig. angle x = 62° angle X Y Z = 56° If YI and ZI
are the bisectors of angle XYZ and angle XZY respectively of triangle XYZ, find angle IZY and angle YIZ?​

Answer 1

Answer:

Given, ∠X=62

∘

,∠XYZ=54

∘

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

According to the question

∠X+∠XYZ+∠XZY=180

∘

(Sum of the interior angles of the triangle.)

⇒62

∘

+54

∘

+∠XZY=180

∘

116

∘

+∠XZY=180

∘

∠XZY=64

∘

Now, ∠OZY=

2

1

∠XZY(ZO is the bisector.)

⇒∠OZY=32

∘

Also ∠OYZ=

2

1

∠XYZ (YO is the bisector.)

⇒∠OYZ=27°

Now, ∠OZY+∠OYZ+∠O=180

∘

(Sum of the interior angles of the triangle.)

⇒32

∘

+27

∘

+∠YOZ=180

∘

⇒59

∘

+∠YOZ=180

∘

⇒∠YOZ=121

∘

Answer 2

Angle IZY = 31 and Angle YIZ = 121