Question

"Question 2 In the given figure, ∠X = 62º, ∠XYZ = 54º. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of ΔXYZ, find ∠OZY and ∠YOZ.

Class 9 - Math - Lines and Angles Page 107"

Answer 1

Bisector of an angle:

A ray which divides an angle into two equal parts is called bisector of an angle.

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Solution:

Given:

∠x=62° & ∠XYZ=54°

In △XYZ, 

∠XYZ+∠YZX+∠ZXY=180∘.      

 

 [Sum of interior angles of a triangle is 180∘]

 

⇒116∘+∠YZX=180∘

⇒∠YZX=180∘−116∘=64∘  …..(i)

 

YO is the bisector of ∠XYZ

 

⇒∠XYO=∠OYZ= 1/2∠XYZ

=1/2(54∘)=27∘  …….(ii)

 

⇒ZO is the bisector of ∠YZX

∴∠XZO=∠OZY=1/2∠YZX

=1/2(64∘)=32∘  ……(iii)

 

 (from equation (i)

 

 =∠OZY=32°

 

In  △OYZ, 

 

∠OYZ+∠OZY+∠YOZ=180∘    

(sum of interior angle of a triangle is 180°)

 

⇒27°+32°+∠YOZ=180∘  

  [using equation (i) and (ii)]

 

⇒59∘+∠YOZ=180∘

 ⇒∠YOZ=180∘−59∘=121∘

 

Hence, ∠YOZ=121° & ∠OZY=32°

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Answer 2

I think you understand it